TW201320717A - Method of displaying 3D image - Google Patents

Abstract

The present invention provides a method of displaying a 3D image, which mainly proposes a real-time detection method of a viewing position, an optimum alignment method of a viewing position and a view, a dynamic multi-view 3D image sythesizing method, and a design method of a static parallax barrier device, to eliminate defects of bare-eye viewing 3D image display especially in the case that a common flat-panel display screen and a static parallax barrier device are used to display a 3D image, so as to effectively solve problems of a ghost image, a pseudo stereoscopic image, and insufficient viewing freedom in horizontal and vertical directions on an optimum viewable plane, thereby achieving the objectives of greatly improving the 3D image quality and the convenience of use.

Description

Translated fromChinese

一種三次元影像顯示之方法Method for displaying three-dimensional image

本發明為一種三次元影像顯示之方法，主要係針對裸眼視三次元影像顯示之缺失，尤其是對於利用一般平面顯示器螢幕與靜態視差光柵裝置以顯示三次元影像時，本發明提出一觀賞位置即時檢測之方法、一觀賞位置與視景最佳對位之方法、一動態多視景3D影像合成之方法與一靜態視差光柵裝置設計之方法，可於最佳可視面上，有效解決鬼影、假立體影像、與水平與垂直方向觀賞自由度不足之問題，達到大幅提高3D影像品質與使用方便性之目的。The invention is a three-dimensional image display method, mainly for the lack of naked-eye view three-dimensional image display, especially for displaying a three-dimensional image by using a general flat display screen and a static parallax barrier device, the present invention proposes an immediate viewing position. The method of detecting, the method of optimally aligning the viewing position and the visual view, the method of synthesizing the dynamic multi-view 3D image and the method of designing the static parallax grating device can effectively solve the ghost image on the optimal visible surface. False stereoscopic images, and the lack of freedom of viewing in horizontal and vertical directions, have greatly improved the quality and ease of use of 3D images.

如中華民國專利申請案號：100114446專利所揭示之一種多視景三次元影像顯示之方法(Method of Displaying Multi-View 3D Image)，針對多視景裸眼式三次元影像之顯示，主要是提出一多視景3D影像合成之方法、與一傾斜條狀視差光柵(Slantwise Strip Parallax Barrier)最佳化之設計，可於最佳觀賞距離上，提供複數個位置為固定之最佳視點，並於該最佳視點處，達到個別呈現單一視景影像之目的。由於該傾斜條狀視差光柵係為一固定之結構(以下統稱”靜態視差光柵裝置”)、且該多視景3D影像合成之方法，係為一固定之合成程序(以下統稱”靜態多視景3D影像合成方法”)，於該單一之最佳視點上，僅能呈現單一且為固定之視景影像。雖然，藉由縮減透光元件之開口寬度，可達到增加水平觀賞自由度之目的。但是，縮減開口寬度除造成影像亮度下降之外，由於所增加之水平觀賞自由度係為有限，並不足以應付較大幅度之觀賞位置之變化。亦即，於水平方向上，當觀賞者之觀賞位置，偏離最佳視點、且超出該水平容許觀賞範圍時，觀賞者會觀看到鬼影(Ghost Image)、或者是左右影像顛倒之假立體影像(Pseudo Stereoscopic Image)，最終造成使用方便性的嚴重不足。另外，對於存在同樣現象的垂直觀賞自由度，卻無任何探討與改善。For example, the Method of Displaying Multi-View 3D Image disclosed in the Patent Application No. 100114446 of the Republic of China, the display of the multi-view naked-eye three-dimensional image is mainly proposed The multi-view 3D image synthesis method and the optimized design of a tilted strip parallax barrier (Slantwise Strip Parallax Barrier) can provide a plurality of positions with a fixed position at an optimal viewing distance, and At the best viewpoint, the purpose of individualizing a single view image is achieved. Since the oblique strip-shaped parallax barrier is a fixed structure (hereinafter collectively referred to as "static parallax barrier device"), and the multi-view 3D image synthesis method is a fixed synthesis program (hereinafter collectively referred to as "static multi-view" The 3D image synthesis method") can only present a single and fixed view image on the single best viewpoint. Although the horizontal viewing freedom can be increased by reducing the opening width of the light transmitting member. However, in addition to reducing the width of the image, in addition to the decrease in image brightness, the increased degree of viewing freedom is limited, and is not sufficient to cope with changes in viewing positions of a large extent. That is, in the horizontal direction, when the viewing position of the viewer deviates from the optimal viewpoint and exceeds the allowable viewing range of the level, the viewer will watch the ghost image (Ghost Image) or the fake stereoscopic image with the left and right images reversed. (Pseudo Stereoscopic Image), which ultimately caused serious shortage of ease of use. In addition, there is no discussion or improvement for the vertical viewing freedom with the same phenomenon.

對於上述習知技藝之缺失，尤其是對於利用一靜態視差光柵裝置與一靜態多視景3D影像合成方法，以呈現三次元影像之缺失，本發明主要提出一靜態視差光柵裝置設計之方法、一動態多視景3D影像合成之方法，並配合一觀賞位置即時檢測方法、與一觀賞位置與視景最佳對位之方法，可於最佳可視面上，有效解決鬼影、假立體影像、與水平與垂直方向觀賞自由度不足之問題，達到大幅提高3D影像品質與使用方便性之目的。For the lack of the above-mentioned prior art, especially for the use of a static parallax barrier device and a static multi-view 3D image synthesis method to present the absence of a three-dimensional image, the present invention mainly proposes a method for designing a static parallax barrier device, The method of dynamic multi-view 3D image synthesis, combined with an instant detection method of viewing position and the best alignment between a viewing position and a visual view, can effectively solve ghost images, fake stereo images, and the best visible surface. The problem of insufficient degree of freedom of viewing in horizontal and vertical directions is to achieve a great improvement in the quality and ease of use of 3D images.

1.靜態視差光柵裝置設計之方法1. Method for designing static parallax barrier device

如圖1所示，係一般R、G、B次畫素為水平條狀排列(Horizontal Strip Configuration)平面顯示器螢幕之示意圖。該平面顯示器螢幕1，係可為一般之液晶螢幕、電漿螢幕、或是OLED螢幕，由N×M個R、G、B次畫素所構成，並具有水平條狀排列之特徵。其中，N為構成該顯示器螢幕水平方向(X軸)次畫素之總數、M則為構成該顯示器螢幕垂直方向(Y軸)次畫素之總數；j、i則各為單一個次畫素水平與垂直位置之編號，其中，0≦j≦N-1;0≦i≦M-1。該單一個次畫素具有P_H×P_V之大小，其中，P_H為次畫素之水平寬度、P_V為次畫素之垂直高度。扣除各次畫素間之黑色間隔2(通常由不發光材料所構成並呈黑色，例如液晶顯示面板上，係由黑色光阻所構成，並稱為Black Matrix)，該單一個次畫素有效發光尺寸則為H×V。所謂水平條狀排列，係指對於任意一條水平掃描線上，該R、G、B次畫素係沿水平方向、且依R、G、B之排列次序，以構成一具顏色分布之條狀結構物；而於垂直方向，則由同一顏色之次畫素，以構成一單色之條狀結構物。為了後文之圖示說明，定義一座標系XYZ，令該座標系之X軸係設置於水平之方向、Y軸係設置於垂直之方向、Z軸則以垂直於該顯示器螢幕1之方向設置，且該三軸之方向遵守右手定則(Right-hand rule)。另外，該座標系XYZ之原點，係可設置於該螢幕之中心。以下，該座標系XYZ，簡稱為螢幕座標系。As shown in FIG. 1 , a general R, G, and B pixel is a schematic diagram of a horizontal strip configuration flat display screen. The flat display screen 1 can be a general liquid crystal screen, a plasma screen, or an OLED screen, and is composed of N×M R, G, and B pixels, and has a horizontal strip arrangement. Where N is the total number of sub-pixels in the horizontal direction (X-axis) of the display screen, and M is the total number of sub-pixels constituting the vertical direction (Y-axis) of the display screen; j and i are each a single pixel. The number of horizontal and vertical positions, where 0≦j≦N-1; 0≦i≦M-1. The single sub-pixel has a size of P_H × P_V , where P_H is the horizontal width of the sub-pixel and P_V is the vertical height of the sub-pixel. After subtracting the black interval 2 between the pixels (usually composed of non-luminescent material and black, for example, the liquid crystal display panel is composed of black photoresist, and is called Black Matrix), the single sub-pixel is effective. The size of the light is H x V. The horizontal strip arrangement means that for any horizontal scanning line, the R, G, and B pixels are in the horizontal direction and in the order of R, G, and B, to form a strip structure with a color distribution. In the vertical direction, the sub-pixels of the same color are used to form a monochromatic strip structure. For the following illustration, define a calibration system XYZ such that the X-axis system of the coordinate system is set in the horizontal direction, the Y-axis system is disposed in the vertical direction, and the Z-axis is disposed in the direction perpendicular to the display screen 1 of the display. And the direction of the three axes follows the right-hand rule. In addition, the origin of the coordinate system XYZ can be set at the center of the screen. Hereinafter, the coordinate system XYZ is simply referred to as a screen coordinate system.

當使用R、G、B次畫素為水平條狀排列之平面顯示器以顯示三次元影像時，根據前述之專利，對於任一多視景影像，係可由n(令n≧2)個單一視景影像V_k所構成。是以，n即為總視景數。另外，可如下定義該單一視景影像V_k：When a flat panel display in which R, G, and B pixels are arranged in a horizontal strip is used to display a three-dimensional image, according to the aforementioned patent, for any multi-view image, it is possible to use n (n≧2) single views. The scene image V_k is composed. Therefore, n is the total number of views. Further, the definition of which may be single view image V_k as follows:

其中，M、N、i、j如前述之定義，k為視景編號數，且0≦k<n：為該單一視景影像V_k中，位於(i,j)位置之次畫素影像資料。另外，對於利用R、G、B次畫素為垂直條狀排列(Vertical Strip Configuration)、馬賽克排列(Mosaic Configuration)、或三角狀排列(Delta Configuration)之顯示器螢幕(無圖示)以顯示多視景影像時，式(1)亦可適用，請參閱中華民國專利申請案號：099127429、099134699。當然，對於為了省電目的所發展出來的Pentile排列(無圖示，具有RGBW，其中W為白色)，亦可透過式(1)，以定義該單一視景影像V_k。本發明中，只以水平條狀排列之顯示器螢幕為例，說明本發明之功效，是以，不再重複贅述。該多視景3D合成影像Σ_n，係可透過以下公式之運算以產生：WhereM ,N , i, j are as defined above, k is the number of view numbers, and 0≦k<n: The sub-pixel image data located at the (i, j) position in the single view image V_k . In addition, for a display screen using a vertical strip configuration, a mosaic configuration (Mosaic Configuration), or a delta arrangement (not shown) using R, G, and B pixels to display multi-view. For the scene image, the formula (1) can also be applied. Please refer to the Republic of China patent application number: 099127429, 099134699. Of course, to save power for the purpose of developed Pentile arrangement (not shown, having the RGBW, where W is white), also through the formula (1), to define the single view image V_k. In the present invention, the display screens arranged in a horizontal strip are taken as an example to illustrate the effects of the present invention, and the detailed description thereof will not be repeated. The multi-view 3D synthetic image Σ_n can be generated by the following formula:

其中，Λ為視景編號數，係由以下公式之運算以產生：Where Λ is the number of view numbers, which is generated by the following formula:

其中，Λ<n;n為總視景數；m為橫向最小顯示單元次畫素構成之數目；Q為縱向最小顯示單元次畫素構成之數目；Δ為橫向位移相位；Π為橫向位移振幅。另外，int係為取整數之函數，Mod則為取餘數之函數。所謂橫向、縱向最小顯示單元，係指透過視差光柵單一透光元件之開口，所能觀看到視景影像之最小單元。另外，對於利用R、G、B次畫素為馬賽克排列、三角狀排列、或Pentile排列之顯示器螢幕(無圖示)，以顯示多視景影像時，式(3)亦可適用，請參閱中華民國專利申請案號：099127429、099134699。本發明中，只以水平條狀排列之顯示器螢幕為例，說明本發明之功效，是以，不再重複贅述。當然，根據式(3)所取得之多視景3D合成影像Σ_n，係具有右傾斜之特徵。對於具有左傾斜特徵之影像合成，則可如下式表示(請參該099127429、099134699專利)：Where Λ<n;n is the total number of views; m is the number of sub-pixels in the horizontal minimum display unit; Q is the number of sub-pixels in the vertical minimum display unit; Δ is the lateral displacement phase; Π is the lateral displacement amplitude . In addition, int is a function of taking integers, and Mod is a function of taking remainders. The so-called horizontal and vertical minimum display unit refers to the smallest unit through which the opening of the single light-transmitting element of the parallax barrier can be viewed. In addition, the formula (3) can also be applied to display a multi-view image using a display screen of R, G, and B pixels in a mosaic arrangement, a triangular arrangement, or a Pentile arrangement (not shown), see also Republic of China patent application number: 099127429, 099134699. In the present invention, the display screens arranged in a horizontal strip are taken as an example to illustrate the effects of the present invention, and the detailed description thereof will not be repeated. Of course, the multi-view 3D synthetic image Σ_n obtained according to the equation (3) has the feature of right tilt. For image composition with left-tilt features, it can be expressed as follows (refer to the patents 099127429, 099134699):

如圖2～圖9所示，係根據式(3)、且在各種不同參數下，所產生具右傾斜特徵之多視景3D合成影像Σ_n。圖上所示之0、1、2、3即為視景編號數。對式(3)代入特殊之參數，如圖10所示，亦可產生一不具傾特徵之多視景3D合成影像Σ_n。另外，根據式(4)，可產生具左傾斜特徵之多視景3D合成影像Σ_n，如圖11所示。以下，為了簡化圖示與說明本發明之功效，首先，主要以n=2、m=3、Q=1、Δ=0、Π=1所構成之具右傾斜特徵雙視景3D合成影像(圖4)為例，說明傾斜條狀視差光柵之結構、視景分離作用、最佳視點空間分佈、與水平與垂直允許觀賞範圍與自由度。As shown in FIGS. 2 to 9, a multi-view 3D composite image Σ_{n having} a right-tilt feature is generated according to the equation (3) and under various parameters. 0, 1, 2, and 3 shown in the figure are the number of view numbers. Substituting the special parameters into the equation (3), as shown in FIG. 10, a multi-view 3D synthetic image Σ_{n having} no tilting characteristics can also be generated. In addition, according to the equation (4), a multi-view 3D composite image Σ_{n having} a left-tilt feature can be generated, as shown in FIG. Hereinafter, in order to simplify the illustration and illustrate the effects of the present invention, firstly, the right-tilt feature dual-view 3D synthetic image consisting of n=2, m=3, Q=1, Δ=0, Π=1 is mainly used ( Fig. 4) is an example for explaining the structure of the oblique strip-shaped parallax barrier, the separation of the view, the spatial distribution of the optimal viewpoint, and the allowable viewing range and degree of freedom with the horizontal and vertical.

如圖12所示，係雙視景用傾斜條狀視差光柵結構之示意圖。該雙視景用傾斜條狀視差光柵310，主要係由多數個傾斜條狀透光元件311、與多數個傾斜條狀遮蔽元件312所構成，並具有水平方向重複交錯排列之特徵。。該透光元件311、遮蔽元件312，個別具有B_H、之水平寬度，並具有一傾斜角度θ。於螢幕座標系下，對於該雙視景3D合成影像Σ_n(圖4)，該雙視景傾斜條狀視差光柵310，係可將該3D合成影像Σ_n，作視景分離之光學作用，且於最佳觀賞距離(Optimum Viewing Distance)Z₀上，提供多數個位置為固定之最佳視點(Optimum Viewing Point)，並於該最佳視點處，作視景分離之光學作用，達到個別呈現單一視景影像之目的。該多數個最佳視點之位置，係可由P_k,i,j(x_c,y_c,Z₀)所定義，如圖13所示。其中，x_c、y_c可如下表示：As shown in FIG. 12, it is a schematic diagram of a tilted strip-shaped parallax barrier structure for a dual view. The double-view oblique strip-shaped parallax barrier 310 is mainly composed of a plurality of oblique strip-shaped light-transmitting elements 311 and a plurality of oblique strip-shaped shielding elements 312, and has a feature of repeating staggered arrangement in the horizontal direction. . The light transmitting element 311 and the shielding element 312 each have B_H , The horizontal width has an inclination angle θ. Under the screen coordinate system, for the dual-view 3D synthetic image Σ_n (Fig. 4), the dual-view oblique strip-shaped parallax barrier 310 can be used for the optical separation of the 3D synthetic image Σ_n . And at the optimal viewing distance (Optimum Viewing Distance) Z₀ , a plurality of Optimum Viewing Points are provided, and at the optimal viewpoint, the optical effect of the visual separation is achieved, and the individual rendering is achieved. The purpose of a single view image. The position of the majority of the best viewpoints can be defined by P_k,i,j (x_c ,y_c ,Z₀ ), as shown in FIG. Where x_c and y_c can be expressed as follows:

x_c=[n×i-(n-1)/2+j-k]×L_H　(5-1)x_c =[n×i-(n-1)/2+jk]×L_H (5-1)

y_c=k×L_V　(5-2)y_c =k×L_V (5-2)

其中，n為總視景數、i為水平可視區編號、j為視景數編號、k為垂直可視區編號、L_H為水平最佳視點間距(Horizontal Interval Between Two Optimum Viewing Points)、L_V為垂直最佳視點間距(Vertical Interval Between Two Optimum Viewing Points)。對於i、j、k、L_H、L_V等參數，如下文之說明。另外，對於所有P_k,i,j(x_c,y_c,Z₀)所存在之面，即Z=Z₀之面，稱為”最佳觀賞面(Optimum Viewing Plane)”。Where n is the total number of views, i is the horizontal viewable area number, j is the view number, k is the vertical viewable area number, and L_H is the horizontal interval Between Two Optimum Viewing Points, L_V Vertical Interval Between Two Optimum Viewing Points. For parameters such as i, j, k, L_H , L_{V ,} etc., as explained below. In addition, the face where all P_k,i,j (x_c ,y_c ,Z₀ ) exist, that is, the face of Z=Z₀ is called "Optimum Viewing Plane".

首先，說明位於y_c=0(即k=0)水平線上之最佳視點P_0,i,j(x_c,y_c,Z₀)產生之原理。First, the principle of the optimal viewpoint P_0,i,j (x_c ,y_c ,Z₀ ) at the horizontal line of y_c =0 (ie, k=0) is explained.

如圖14所示，係雙視景3D合成影像顯示原理之示意圖。對於顯示於該平面顯示器螢幕1上之雙視景3D合成影像(即由所構成之影像。其中，令為左影像、為右影像)，該雙視景用傾斜條狀視差光柵310，係可於最佳觀賞距離Z₀、且於水平方向上之多數最佳視點P_0,-1,1、P_0,0,0、P_0,0,1、P_0,1,0處(該各最佳視點間之水平距離，即構成水平最佳視點間距L_H)，將該雙視景3D合成影像，個別分離成等單一視景影像。為了在Z₀處達到上述視景分離之功效，該構成雙視景用傾斜條狀視差光柵310之B_H、、L_H、θ，必須如下式設計：As shown in FIG. 14, it is a schematic diagram of the principle of dual view 3D synthetic image display. For a dual view 3D composite image displayed on the flat display screen 1 (ie by The image formed. Among them, order For the left image, The right-view image uses the oblique strip-shaped parallax barrier 310 for the optimal viewing distance Z₀ and the most optimal viewpoints P_0,-1,1 , P_0,0 in the horizontal direction.₀ , P_0,0,1 , P_0,1,0 (the horizontal distance between the best viewpoints, that is, the horizontal optimal viewpoint spacing L_H ), the two-view 3D composite images are separately separated into A single view image. In order to achieve the above-described effect of visual separation at Z₀ , the B_{H of the} oblique strip-shaped parallax barrier 310 constituting the dual view is , L_H , θ, must be designed as follows:

且必須將由式(6)～式(9)所構成之傾斜條狀視差光柵310裝置在Z=L_B處。該Z₀與L_B之關係，如下式：Further, the inclined strip parallax barrier 310 composed of the equations (6) to (9) must be placed at Z = L_B . The relationship between Z₀ and L_B is as follows:

另外，式(6)、(8)亦可如下表示：In addition, the formulas (6) and (8) can also be expressed as follows:

上述式(6)～式(12)，亦適用於垂直條狀式視差光柵、傾斜格狀式視差光柵、垂直柱狀透鏡陣列、傾斜柱狀透鏡陣列、與傾斜格狀微柱狀透鏡陣列之設計(請參閱中華民國專利申請案號：098128986、099107311、099108528、099127429、099128602、099134699)。對於上述各種視差光柵、柱狀透鏡陣列等視景分離裝置，因具有一不可變光學結構之特徵(如視差光柵透光元件之寬度與裝置之位置)之視景分離裝置，通稱為”靜態視景分離裝置”。當然，上述有關於水平方向視差光柵光學結構之設計，式(6)～式(12)，以及，垂直方向視差光柵光學結構之設計(如後文所述)，亦適用於中華民國專利申請案號：098145946中所開示之動態液晶視差光柵之設計。The above formulas (6) to (12) are also applicable to a vertical strip type parallax barrier, a tilt grid type parallax barrier, a vertical cylindrical lens array, a tilted cylindrical lens array, and an inclined lattice micro cylindrical lens array. Design (please refer to the Republic of China patent application number: 098128986, 099107311, 099108528, 099127429, 099128602, 099134699). For the above-mentioned various kinds of parallax barriers such as parallax barriers and lenticular lens arrays, the visual separation device having the characteristics of an invariable optical structure (such as the width of the parallax barrier light transmitting member and the position of the device) is generally referred to as "static viewing". Scene separation device". Of course, the above is related to the design of the optical structure of the horizontal direction parallax barrier, the design of the equations (6) to (12), and the optical structure of the vertical direction parallax barrier (as described later), also applicable to the patent application of the Republic of China. No.: 098145946 Designed for dynamic liquid crystal parallax barriers.

另外，對於如圖14所示之原理圖示，式(6)～式(9)中，係令n=2、m=3、Q=1。一般，於視差光柵之設計上，會令該水平最佳視點間距L_H，係等於雙眼平均間距(Iinterpupillary Distance,簡稱IPD)L_E，亦即，可令：Further, in the equations shown in Fig. 14, in the equations (6) to (9), it is assumed that n = 2, m = 3, and Q = 1. Generally, in the design of the parallax barrier, the optimal viewpoint distance L_{H of} the level is equal to the average inter-ocular distance (IPD) L_E , that is, it can be:

L_H=L_E　(13)L_H =L_E (13)

以下，亦可以L_E代表水平最佳視點間距L_H。是以，只要觀賞者將其左右眼10、11個別置放於適當處，如(P_0,0,0、P_0,0,1)，即可觀賞到無鬼影之3D影像，該2個最佳視點P_0,0,0、P_0,0,1，係構成一組可視區(Viewing Zone)。是以，根據圖14所示之基本原理，可更進一步說明最佳視點P_k,i,j(x_c,y_c,Z₀)中i、j之定義。Hereinafter, L_E may also represent the horizontal optimum viewpoint distance L_H . Therefore, as long as the viewer places the left and right eyes 10, 11 individually, such as (P_0,0,0 , P_0,0,1 ), the 3D image without ghosts can be viewed. The best viewpoints P_0,0,0 , P_0,0,1 form a set of viewing zones. Therefore, according to the basic principle shown in FIG. 14, the definition of i, j in the optimum viewpoint P_{k, i, j} (x_c , y_c , Z₀ ) can be further explained.

如圖15所示，i為可視區之編號(Zone Number)，係為一整數；j為視景之編號(View Number)，係為一包含零之正整數、且j<n。當i=0時，係為正對螢幕正中心位置之可視區、i>0為分布在螢幕右邊位置之可視區、i<0則分布在螢幕左邊位置之可視區；當n=2時，j=0時為左影像、j=1為右影像。是以，根據式(5-1)、k=0，可計算取得i=0、i=±1、i=±2、i=±3等各可視區中，各水平最佳視點之座標x_c，如圖16所示。其中，x_c之長度係以L_E為單位表示之。另外，如圖17～圖18所示，係n=4，i=0、i=±1等各可視區中，各水平最佳視點之位置與座標之示意圖。其中，j=0代表最左之影像，j=3代表最右之影像。當左、右眼10、11之觀看位置，係個別對準於同一可視區內相鄰之最佳視點時，係可觀賞到正確之三次元影像；若所對準之最佳視點，係屬於不同可視區內之最佳視點時，則觀看到假立體之三次元影像。As shown in FIG. 15, i is a zone number, which is an integer; j is a view number, which is a positive integer containing zero, and j<n. When i=0, it is the visible area facing the center of the screen, i>0 is the visible area distributed on the right side of the screen, and i<0 is the visible area of the left side of the screen; when n=2, When j=0, it is the left image, and j=1 is the right image. Therefore, according to the equations (5-1) and k=0, the coordinates x of each horizontal optimal viewpoint in each visible area such as i=0, i=±1, i=±2, and i=±3 can be calculated and calculated._c , as shown in Figure 16. Wherein, the length of x_c is expressed in units of L_E . Further, as shown in FIGS. 17 to 18, a map of the position and coordinates of each horizontal optimum viewpoint in each of the visible regions such as n=4, i=0, and i=±1. Where j=0 represents the leftmost image and j=3 represents the rightmost image. When the viewing positions of the left and right eyes 10, 11 are individually aligned with the best viewpoints adjacent to each other in the same viewing area, the correct three-dimensional image can be viewed; if the best viewpoint is aligned, When the best viewpoint is in different visible areas, the three-dimensional image of the fake stereo is viewed.

以下，說明透光元件開口水平寬度之縮減與水平觀賞自由度(Horizontal Viewing Freedom)之關係。根據中華民國專利申請案號：098128986、099107311中所揭露之視差光柵水平開口元件最佳化之方法，亦即利用適當縮減開口寬度之方法，可達到解決水平方向上直接性鬼影之現象、並增加水平觀賞自由度(Degree of Horizontal Viewing Freedom)之目的。Hereinafter, the relationship between the reduction in the horizontal width of the light-transmitting element opening and the horizontal viewing degree (Horizontal Viewing Freedom) will be described. According to the method for optimizing the horizontal opening element of the parallax barrier disclosed in the Patent Application No. 098128986 and 099107311, that is, the method of appropriately reducing the width of the opening can solve the phenomenon of direct ghosting in the horizontal direction, and Increase the purpose of Degree of Viewing Freedom.

根據中華民國專利申請案號：099107311，水平容許觀賞範圍(Allowable Horizontal Viewing Range) Δ X_VF、與透光元件開口水平寬度之縮減量Δ B_H之關係，係由下式所定義：According to the Republic of China Patent Application No. 099107311, the relationship between the Allowable Horizontal Viewing Range Δ X_VF and the reduction in the horizontal width of the opening of the light-transmitting element Δ B_H is defined by the following formula:

其中，B_H、L_E如前述之定義。另外，定義水平觀賞自由度R_x，如下式：Wherein, B_H and L_{E are} as defined above. In addition, define the horizontal viewing degree of freedom R_x as follows:

R_x=Δ B_H/B_H　(15)R_x =Δ B_H /B_H (15)

因0≦Δ B_H≦B_H，所以，0≦R_x≦1。另外，將式(14)代入式(15)，可得Since 0 ≦ Δ B_H ≦ B_H , 0 ≦ R_x ≦ 1. In addition, the formula (14) is substituted into the formula (15), which is available.

ΔX_VF=R_x×L_E　(16)ΔX_VF =R_x ×L_E (16)

如圖19所示，係透光元件開口水平寬度之縮減量ΔB_H=B_H/2時，水平容許觀賞範圍ΔX_VF之示意圖。當ΔB_H=B_H/2時，可得R_x=0.5、ΔX_VF=0.5L_E。如圖20所示，當ΔB_H=2B_H/3時，可得ΔR_x=2/3、X_VF=2L_E/3。所謂”水平容許觀賞範圍”，係指在最佳視點處，當於水平方向改變觀賞位置時，於不發生鬼影之條件下，所允許最大水平移動之範圍。而”水平觀賞自由度”，即相對於雙眼平均間距L_E，定義一介於0與1之數值，以評估水平觀賞方便性之程度。亦即，該R_x值愈大，可得愈大水平容許觀賞範圍，亦即愈方便觀賞。另外，為了更精確描述該水平容許觀賞範圍之位置，對於任一水平最佳視點P_k,i,j，再定義_HP_k,i,j⁺(x_c+Δx_H,y_c,Z₀)、_HP_k,i,j^-(x_c-Δx_H,y_c,Z₀)等兩位置，以描述該水平容許觀賞範圍兩端點之位置。令Δx_H為半水平容許觀賞範圍，且Δx_H可如下式表示：As shown in FIG. 19, it is a schematic diagram of the horizontal allowable viewing range ΔX_VF when the reduction amount of the horizontal width of the light-transmitting element opening is ΔB_H = B_H /2 . When ΔB_H = B_H /2, R_x = 0.5 and ΔX_VF = 0.5 L_{E are obtained} . As shown in Fig. 20, when ΔB_H = 2B_H /3, ΔR_x = 2/3 and X_VF = 2L_E /3 are obtained. The so-called "horizontal allowable viewing range" refers to the range of maximum horizontal movement allowed under the condition that ghosting does not occur when the viewing position is changed in the horizontal direction at the optimal viewpoint. The "horizontal viewing degree of freedom", that is, relative to the average distance L_{E of the} eyes, defines a value between 0 and 1 to assess the degree of horizontal viewing convenience. That is, the larger the R_x value, the larger the level of viewing can be obtained, that is, the more convenient it is to watch. In addition, in order to more accurately describe the position of the horizontal allowable viewing range, for any horizontal optimal viewpoint P_k,i,j , then_H P_k,i,j⁺ (x_c +Δx_H ,y_c ,Z₀ ),_H P_k,i,j^- (x_c -Δx_H , y_c , Z₀ ) and other two positions to describe the position of the points at the ends of the allowable viewing range. Let Δx_H be a semi-level allowable viewing range, and Δx_H can be expressed as follows:

Δx_H=ΔX_VF/2=R_x×L_E/2　(17)Δx_H =ΔX_VF /2=R_x ×L_E /2 (17)

是以，如圖19、圖20所示，該水平容許觀賞範圍321(亦即，水平無鬼影區)，係可由下式所定義：Therefore, as shown in FIG. 19 and FIG. 20, the horizontal allowable viewing range 321 (that is, the horizontal ghost-free area) can be defined by the following formula:

_HP_k,i,j^-≦x≦_HP_k,i,j⁺　(18)_H P_k,i,j^- ≦x≦_H P_k,i,j⁺ (18)

對於存在於同一可視區內之水平鬼影區322，係可由下式所定義：For the horizontal ghost area 322 existing in the same visible area, it can be defined by the following formula:

_HP_k,i,j⁺＜x＜_HP_k,i,j+1^-　(19)_H P_k,i,j⁺ <x<_H P_k,i,j+1^- (19)

其中，0≦j≦n-2；對於存在於相鄰可視區內之水平鬼影區323，則可由下式所定義：Where 0,j≦n-2; for the horizontal ghost region 323 existing in the adjacent visible region, it can be defined by:

_HP_k,i-1,n-1⁺＜x＜_HP_k,i,0^-　(20)_H P_k,i-1,n-1⁺ <x<_H P_k,i,0^- (20)

綜上所述，由於該傾斜條狀視差光柵(含所有靜態視景分離裝置)，係為一固定之結構、且所利用之該靜態多視景3D影像合成方法，係在螢幕上之固定位置，以產生及顯示該多視景3D合成影像。是以，當觀賞者雙眼之位置，偏離最佳視點、且超出該水平容許觀賞範圍321時，觀賞者會觀看到鬼影、甚至是觀看到左右影像顛倒之假立體影像，以致造成觀賞不便(無法大幅度水平移動頭部)、3D影像品質低下等問題，最終產生頭昏之現象(鬼影嚴重、或觀看到假立體影像時，人腦無法將左右影像，合成為一立體影像)。In summary, the oblique strip-shaped parallax barrier (including all static view separation devices) is a fixed structure, and the static multi-view 3D image synthesis method utilized is fixed on the screen. To generate and display the multi-view 3D composite image. Therefore, when the position of the viewer's eyes deviates from the optimal viewpoint and exceeds the allowable viewing range of 321 , the viewer will watch the ghosts and even watch the fake stereoscopic images with the left and right images reversed, resulting in inconvenient viewing. (The head cannot be moved horizontally), the quality of 3D images is low, and the like, and eventually the phenomenon of dizziness (when the ghost is serious, or when the fake stereoscopic image is viewed, the human brain cannot synthesize the left and right images into a stereoscopic image).

以下，說明垂直方向之光學作用。對於式(5-1)、(5-2)中，當y_c≠0(即k≠0)時，如圖13所示，該最佳視點P_k≠0,i,j(x_c,y_c,Z0)之分佈位置，亦如y_c=0(即k=0)時，P_k=0,i,j(x_c,y_c,Z₀)之分佈位置。事實上，於垂直方向上最佳視點P_k≠0,i,j(x_c,y_c,Z₀)之分佈位置，係將所有P_k=0,i,j(x_c,y_c,Z₀)，延傾斜角度θ做一斜線之位移。當該斜線位移量之水平分量，係等於一個L_H(=L_E)時，該斜線位移量之垂直分量係為L_V。是以，對於位於起始觀賞位置之觀賞者而言，如觀賞者之左眼係位於P_k=0,i=0,j=0(x_c=-0.5L_E,y_c=0,Z₀)，當該觀賞者延垂直方向改變觀賞位置、且位置移動量達一個+L_V時，該觀賞者左眼之位置係變成為P_k=1,i=0,j=1(x_c=-0.5L_E,y_c=L_V,Z₀)。亦即，於垂直方向改變觀賞位置時，因垂直方向亦有視景分離之功效，即每隔一垂直最佳視點間距L_V距離，就會觀看到不同之單一視景。是以，對於具傾斜結構之視景分離裝置，其最佳視點P_k,i,j之分佈，對於亦具有同樣傾斜之特徵。Hereinafter, the optical action in the vertical direction will be described. For equations (5-1) and (5-2), when y_c ≠ 0 (ie, k ≠ 0), as shown in FIG. 13, the optimal viewpoint P_{k ≠ 0, i, j} (x_c , The distribution position of y_c , Z0) is also the distribution position of P_{k=0, i, j} (x_c , y_c , Z₀ ) when y_c =0 (ie, k=0). In fact, the distribution of the best viewpoint P_{k ≠ 0, i, j} (x_c , y_c , Z₀ ) in the vertical direction is all P_{k = 0, i, j} (x_c , y_c , Z₀ ), the inclination angle θ is shifted by a diagonal line. When the horizontal component of the oblique line displacement is equal to one L_H (= L_E ), the vertical component of the oblique line displacement is L_V . Therefore, for the viewer at the initial viewing position, for example, the viewer's left eye is at P_{k=0, i=0, j=0} (x_c =-0.5L_E , y_c =0, Z₀ ), when the viewer changes the viewing position in the vertical direction and the position shift amount reaches +L_V , the position of the viewer's left eye becomes P_{k=1, i=0, j=1} (x_c =-0.5L_E , y_c = L_V , Z₀ ). That is, when the viewing position is changed in the vertical direction, since the vertical direction also has the effect of separating the scenes, that is, every other vertical optimum viewpoint spacing L_V distance, a different single viewing angle is observed. Therefore, for a view separating device having a tilted structure_, the distribution of the optimum viewpoints P_{k, i, j} has the same inclination characteristics.

以下，說明垂直方向視景分離之光學作用、透光元件開口垂直寬度之縮減、與垂直觀賞自由度(Vertical Viewing Freedom)之關係。Hereinafter, the optical action in the vertical direction view separation, the reduction in the vertical width of the light-transmitting element opening, and the relationship between the vertical viewing degree and the vertical viewing degree will be described.

由於視景分離裝置，具有水平與垂直方向視景分離之光學作用，對於式(3)、(4)所產生之多視景3D合成影像Σ_n，該視景分離裝置之作用，係對該3D合成影像中，於水平與垂直方向皆具週期分佈之單一視景影像，做視景分離之作用。如圖21～26所示，係由各種不同參數所構成之多視景3D合成影像Σ_n。該影像Σ_n中，各單一視景影像具有水平與垂直週期分佈之特徵，其中，該任一次畫素上所顯示之數字(0、1、2、3)，係代表單一視景影像之編號數。是以，在多視景3D合成影像Σ_n上，該任一單一視景之影像，於水平方向上，係以m×n個次畫素為單位，做一週期性之排列；而於垂直方向上，則以係以m×Q×n個次畫素為單位，做一週期性之排列。當然，垂直方向之光學作用，亦遵守前述水平方向光學公式所規範之光學行為。是以，透光元件垂直開口寬度B_V、垂直最佳視點間距L_V，係可由下式計算取得：Since the visual separation device has an optical effect of separating the horizontal and vertical directions, for the multi-view 3D synthetic image Σ_n generated by the equations (3) and (4), the effect of the visual separation device is In 3D synthetic images, a single view image with periodic distribution in both horizontal and vertical directions serves as a separation of views. As shown in Figs. 21 to 26, a multi-view 3D composite image Σ_n composed of various parameters is used. In the image Σ_n , each single view image has a horizontal and vertical period distribution, wherein the number (0, 1, 2, 3) displayed on the first pixel represents the number of the single view image. number. Therefore, on the multi-view 3D synthetic image Σ_n , the image of any single view is arranged in a periodic direction in units of m×n sub-pixels in the horizontal direction; In the direction, the sequence is arranged in units of m × Q × n sub-pixels. Of course, the optical action in the vertical direction also follows the optical behavior as specified by the aforementioned horizontal optical formula. Therefore, the vertical opening width B_V and the vertical optimum viewpoint spacing L_{V of the} light transmitting element can be calculated by the following formula:

令式(21)除以式(11)，可得B_V與B_H之關係，如下：Dividing equation (21) by equation (11) gives the relationship between B_V and B_H as follows:

令式(22)除以式(8)，可得L_V與L_E之關係，如下：Dividing equation (22) by equation (8) gives the relationship between L_V and L_E as follows:

將式(9)帶入式(24)，可得Bring the formula (9) into the formula (24), which is available.

如圖27所示，係雙視景用傾斜條狀視差光柵垂直方向光學作用之示意圖。對於垂直容許觀賞範圍與自由度之解析，如圖28所示，係透光元件開口垂直寬度之縮減量ΔB_V=B_V/2時，垂直容許觀賞範圍(Allowable Vertical Viewing Range)ΔY_VF之示意圖。如圖29所示，係透光元件開口垂直寬度之縮減量ΔB_V=2B_V/3時，垂直容許觀賞範圍ΔY_VF之示意圖。如前述，該垂直容許觀賞範圍ΔY_VF、與透光元件開口垂直寬度之縮減量ΔB_V之關係，係由下式所定義：As shown in Fig. 27, it is a schematic diagram of the optical action in the vertical direction of the oblique strip-shaped parallax barrier for the dual view. For the analysis of the vertical allowable viewing range and the degree of freedom, as shown in FIG. 28, when the reduction amount of the vertical width of the opening of the light transmitting element is ΔB_V = B_V /2, the vertical allowable viewing range (ΔY_VF ) is schematically shown. . As shown in Fig. 29, a schematic diagram of the vertical allowable viewing range ΔY_VF when the reduction amount of the vertical width of the opening of the light transmitting element is ΔB_V = 2B_V /3. As described above, the relationship between the vertical allowable viewing range ΔY_VF and the reduction amount ΔB_V of the vertical width of the opening of the light transmitting element is defined by the following formula:

其中，B_V、L_V如前述之定義。另外，定義垂直觀賞自由度R_Y，如下式：Wherein, B_V and L_{V are} as defined above. In addition, define the vertical viewing degree of freedom R_Y as follows:

R_Y=ΔB_V/B_V　(27)R_Y =ΔB_V /B_V (27)

因0≦ΔB_V≦B_V，所以，0≦R_Y≦1。另外，將式(27)代入式(26)，可得Since 0 ≦ ΔB_V ≦ B_V , 0 ≦ R_Y ≦ 1. In addition, substituting equation (27) into equation (26) is available.

ΔY_VF=R_Y×L_V　(28)ΔY_VF =R_Y ×L_V (28)

另外，式(16)除以式(28)，可得In addition, the equation (16) is divided by the equation (28),

可令R_x=R_Y，且將式(25)代入式(29)，可得Let R_x =R_Y and substitute equation (25) into equation (29).

同樣地，為了更精確描述該垂直容許觀賞範圍之位置，對於任一水平最佳視點P_k,i,j，再定義_VP_k,i,j⁺(x_c,y_c+Δy_V,Z₀)、_VP_k,i,j^-(x_c,y_c-Δy_V,Z₀)等兩位置，以描述該垂直容許觀賞範圍兩端點之位置。其中，令Δy_V為半垂直容許觀賞範圍，且Δy_V可如下式表示：Similarly, in order to more accurately describe the position of the vertical allowable viewing range, for any horizontal optimal viewpoint P_k,i,j , then_V P_k,i,j⁺ (x_c ,y_c +Δy_V ,Z Two positions, such as₀ ),_V P_k,i,j^- (x_c , y_{c -} Δy_V , Z₀ ), are used to describe the positions of the points at both ends of the vertical allowable viewing range. Where Δy_V is a semi-perpendicular allowable viewing range, and Δy_V can be expressed as follows:

Δy_V=ΔY_VF/2=R_Y×L_V/2　(31)Δy_V = ΔY_VF /2=R_Y × L_V /2 (31)

是以，如圖28、圖29所示，該垂直容許觀賞範圍331(亦即，垂直無鬼影區)，係可由下式所定義：Therefore, as shown in FIG. 28 and FIG. 29, the vertical allowable viewing range 331 (that is, the vertical ghost-free area) can be defined by the following formula:

_vP_k,i,j^-≦y≦_vP_k,i,j⁺　(32)_v P_k,i,j^- ≦y≦_v P_k,i,j⁺ (32)

而垂直鬼影區332，則可由下式所定義：The vertical ghost area 332 can be defined by the following formula:

_vP_k,i,j⁺<y<_vP_k+l,i’,j,　(33)_v P_k,i,j⁺ <y<_v P_k+l,i',j, (33)

其中，當j<n-1時，i’=i、j’=j+1；當j=n-1時，i’=i+1、j’=0。Here, when j < n-1, i' = i, j' = j + 1; when j = n - 1, i' = i + 1, j' = 0.

如上所述，根據式(5-1)～(5-2)、(18)～(20)、(32)～(33)所定義，對於任一最佳視點P_k,i,j(x_c,y_c,Z₀)，如圖30所示，皆存在一水平與垂直之容許觀賞範圍。由於，視景分離裝置具有光學傾斜之特徵，是以，該上述之容許觀賞範圍與鬼影區，係可延該傾斜角θ做一分佈，如圖31所示，最終構成一傾斜帶狀之容許觀賞範圍341、與一傾斜帶狀之鬼影區342，該傾斜帶狀之容許觀賞範圍341、與該傾斜帶狀之鬼影區342，如同該視差光柵310光學結構之特徵，亦具有水平方向重複交錯排列之特徵。對於上述該傾斜帶狀之容許觀賞範圍341，係可定義一中心線Y_i,j(x,y)，如下式：As described above, for any optimal viewpoint P_k,i,j (x) as defined by equations (5-1) to (5-2), (18) to (20), and (32) to (33)_c , y_c , Z₀ ), as shown in Fig. 30, there is a horizontal and vertical allowable viewing range. Since the visor separating device has the feature of optical tilting, the allowable viewing range and the ghosting region can be extended by the tilt angle θ, as shown in FIG. 31, and finally constitute an inclined strip shape. The allowable viewing range 341 and the slanted strip-shaped ghosting area 342, the oblique band-shaped allowable viewing range 341 and the oblique strip-shaped ghosting area 342, as well as the optical structure of the parallax barrier 310, also have a level The direction repeats the characteristics of the staggered arrangement. For the above-mentioned oblique band-shaped allowable viewing range 341, a center line Y_i,j (x,y) can be defined, as follows:

y=f(θ){x-[n×i-(n-1)/2+j]×L_E}　(34)y=f(θ){x-[n×i-(n-1)/2+j]×L_E } (34)

該中心線Y_i,j(x,y)係通過所有具有相同i、j之最佳視點P_k,i,j(x_c,y_c,Z₀)。另外，該傾斜帶狀之容許觀賞範圍341、與傾斜帶狀之鬼影區342間之邊界，係可由邊界線Y_i,j⁺(x,y)、Y_i,j^-(x,y)以構成。其中，Y_i,j⁺(x,y)可由下式表示：The center line Y_i,j (x,y) passes through all the best viewpoints P_k,i,j (x_c ,y_c ,Z₀ ) having the same i,j. In addition, the boundary between the allowable viewing range 341 of the inclined strip shape and the ghosted area 342 of the oblique strip shape may be a boundary line Y_i,j⁺ (x,y), Y_i,j^- (x,y) To constitute. Where Y_i,j⁺ (x,y) can be expressed by the following formula:

y=f(θ){x-[n×i-(n-1)/2+j+R_x/2]×L_E}　(35)y=f(θ){x-[n×i-(n-1)/2+j+R_x /2]×L_E } (35)

Y_i,j^-(x,y)則由下式表示：Y_i,j^- (x,y) is represented by the following formula:

y=f(θ){x-[n×i-(n-1)/2+j-R_x/2]×L_E}　(36)y=f(θ){x-[n×i-(n-1)/2+jR_x /2]×L_E } (36)

對於具右傾斜結構之視景分離裝置，該f(θ)可由下式表示：For a view separating device having a right inclined structure, the f(θ) can be expressed by the following formula:

f(θ)=-tanθ　(37)f(θ)=-tanθ (37)

對於具左傾斜結構之視景分離裝置，該f(θ)則由下式表示：For a view separating device having a left inclined structure, the f(θ) is represented by the following formula:

f(θ)=tanθ　(38)f(θ)=tanθ (38)

另外，當θ=0(即tanθ=0)時，該視景分離裝置即具有垂直結構之特徵(以下稱為具垂直結構之視景分離裝置)，該Y_i,j(x,y)、Y_i,j⁺(x,y)、Y_i,j^-(x,y)則成為垂直線，可個別由下式表示：In addition, when θ=0 (ie, tan θ=0), the view separating device has a feature of a vertical structure (hereinafter referred to as a view separating device having a vertical structure), the Y_i,j (x,y), Y_i,j⁺ (x,y), Y_i,j^- (x,y) are vertical lines, which can be expressed by the following formula:

x=[n×i-(n-1)/2+j]×L_E　(39)x=[n×i-(n-1)/2+j]×L_E (39)

x=[n×i-(n-1)/2+j+R_x/2]×L_E　(40)x=[n×i-(n-1)/2+j+R_x /2]×L_E (40)

x=[n×i-(n-1)/2+j-R_x/2]×L_E　(41)x=[n×i-(n-1)/2+jR_x /2]×L_E (41)

事實上，對於式(34)～(36)所描述之該中心線Y_i,j(x,y)、邊界線Y_i,j⁺(x,y)、Y_i,j^-(x,y)，當令y=0時，所取得之x值，係如式(39)～(41)所示。亦即，對於具傾斜結構、與垂直結構之視景分離裝置，在z=Z₀、y=0之水平線上，係具有相同之視景分離之光學作用。或者，可更簡單地說，傾斜結構、與垂直結構，具有相同之光學作用，其不同處，只在於傾斜角度。以下，該z=Z₀、y=0之水平線，簡稱為最佳觀賞線(Optimum Viewing Line)。如上述，對於具任意傾斜結構之視景分離裝置，於最佳觀賞距離上，式(34)～(41)，係可清楚定義了所有容許觀賞範圍之中心線與邊界線。是以，對於上述所用”傾斜帶狀容許觀賞範圍”、”傾斜帶狀鬼影區”之術語，以下，簡稱為”容許觀賞區”、”鬼影區”；而對於上述所有最佳視點、容許觀賞區之中心線與邊界線等所存在之平面(即Z=Z₀)，簡稱為最佳觀賞面(Optimum Viewing Plane)。In fact, for the center line Y_i,j (x,y) described by equations (34)-(36), the boundary line Y_i,j⁺ (x,y), Y_i,j^- (x,y When y = 0, the obtained x value is as shown in equations (39) to (41). That is, for a view separating device having an inclined structure and a vertical structure, the optical effect of the same visual separation is obtained on the horizontal line of z=Z₀ and y=0. Alternatively, it can be more simply said that the inclined structure has the same optical effect as the vertical structure, and the difference is only the inclination angle. Hereinafter, the horizontal line of z=Z₀ and y=0 is simply referred to as an Optimum Viewing Line. As described above, for the view separating device having an arbitrary inclined structure, the center line and the boundary line of all the allowable viewing ranges can be clearly defined in the optimum viewing distance, the equations (34) to (41). Therefore, the terms "inclined band-shaped allowable viewing range" and "inclined band-shaped ghost area" as used above are hereinafter referred to as "allowable viewing area" and "ghost area"; and for all of the above-mentioned best viewpoints, The plane where the center line and the boundary line of the viewing area are allowed to exist (ie, Z=Z₀ ) is simply referred to as the Optimum Viewing Plane.

如上所述，對於利用具任意傾斜結構之靜態視景分離裝置、及靜態多視景3D影像合成方法，以顯示三次元影像時，於最佳觀賞面上，如圖31所示，該容許觀賞區341與鬼影區342，係由公式(34)～(41)所規範。對於位於最佳觀賞面上之觀賞者，當該觀賞者左右眼之位置，偏離該容許觀賞區341(亦即，進入該鬼影區342)時，觀賞者會觀看到鬼影。另外，觀賞者左右眼之位置，係位於不同之可視區內時，觀賞者會觀看假立體影像。針對上述之特徵，亦即對於利用具任意傾斜結構之靜態視景分離裝置、及靜態多視景3D影像之合成，以顯示三次元影像之方法，以下，簡稱為靜態三次元影像顯示方法(Static Displaying Method of 3D Image)。As described above, for a static view separation device having an arbitrary tilt structure and a static multi-view 3D image synthesis method, when displaying a three-dimensional image, on the optimal viewing surface, as shown in FIG. 31, the allowable viewing is as shown in FIG. The area 341 and the ghost area 342 are specified by the formulas (34) to (41). For the viewer on the best viewing surface, when the position of the left and right eyes of the viewer deviates from the allowable viewing area 341 (ie, enters the ghost area 342), the viewer will see the ghost. In addition, when the position of the left and right eyes of the viewer is in different visible areas, the viewer will watch the fake stereoscopic image. For the above features, that is, a method for displaying a three-dimensional image by using a static view separating device with an arbitrary tilt structure and a composite of a static multi-view 3D image, hereinafter, simply referred to as a static three-dimensional image display method (Static) Displaying Method of 3D Image).

2.動態多視景3D影像合成之方法2. Dynamic multi-view 3D image synthesis method

接下來，說明”動態多視景3D影像之合成”。對於式(3)、式(4)所述多視景3D影像合成之方法，其中n、m、Q、Π等參數，因跟靜態視景分離裝置之硬體結構設計有關，是不隨時間而改變之常數。對於如圖4所示，n=2、m=3、Q=1、Π=1、Δ=0之雙視景3D合成影像，令Δ從1～6變化時，即可得圖32～37所示之雙視景3D合成影像Σ_n(Δ=1)～Σ_n(Δ=6)。該橫向位移相位Δ>0時，即代表各視景之所有次畫素影像資料，以次畫素為單位，向右位移Δ個次畫素，且具有n×m之週期，即Δ=6與Δ=0具有相同之3D影像合成結構。當然，Δ<0，係代表次畫素影像資料，達到向左位移之目的。由於週期性之關係，Δ=A(向右位移A個次畫素)與Δ=A-n×m(向左位移n×m-A個次畫素)具有相同3D影像合成之結構。是以，不再做圖示說明。Next, the description "synthesis of dynamic multi-view 3D video images" will be described. For the multi-view 3D image synthesis method according to the formulas (3) and (4), wherein n, m, Q, Π and other parameters are related to the hardware structure design of the static view separation device, it is not time-dependent. And change the constant. For the dual-view 3D composite image with n=2, m=3, Q=1, Π=1, and Δ=0 as shown in FIG. 4, when Δ is changed from 1 to 6, the graphs 32 to 37 can be obtained. The dual view 3D synthetic image shown Σ_n (Δ=1) ~ Σ_n (Δ = 6). When the lateral displacement phase Δ>0, it represents all the secondary pixel image data of each view. In the sub-pixels, the Δ sub-pixels are shifted to the right, and have a period of n×m, that is, Δ=6 and Δ=0 have the same 3D image synthesis structure. Of course, Δ<0 means the sub-pixel image data. , to achieve the purpose of shifting to the left. Due to the periodic relationship, Δ=A (displaces A sub-pixels to the right) and Δ=An×m (displaces n×mA sub-pixels to the left) have the same structure of 3D image synthesis. Therefore, no longer illustrated.

如上述，所謂”動態多視景3D影像之合成”，係令橫向位移相位Δ為一變數，例如為一時間之函數，可於特定時間點所發生之特定條件下(如後述)，以設定Δ(t)之值。是以，式(3)、式(4)可如下式所示：As described above, the so-called "combination of dynamic multi-view 3D images" is such that the lateral displacement phase Δ is a variable, for example, a function of time, which can be set under specific conditions (as described later) at a specific time point. The value of Δ(t). Therefore, equations (3) and (4) can be expressed as follows:

相較於前述靜態三次元影像顯示方法，由於，本發明之方法，係適用於以時間為變數之三次元影像之顯示，是以，係可歸屬於一種動態三次元影像顯示之方法(Dynamic Displaying Method of 3D Image)。以下，為簡化數學公式之表示，對於與時間有關之相關參數，不再明示其為時間之函數。例如：橫向位移相位、以及如後述之左右眼之座標值。Compared with the foregoing static three-dimensional image display method, since the method of the present invention is applicable to the display of a three-dimensional image with time as a variable, it is a method that can be attributed to a dynamic three-dimensional image display (Dynamic Displaying). Method of 3D Image). In the following, in order to simplify the representation of the mathematical formula, the time-dependent related parameters are no longer explicitly expressed as a function of time. For example, the lateral displacement phase and the coordinate values of the left and right eyes as will be described later.

3.觀賞自由度最佳化之方法3. Method of optimizing the degree of freedom of viewing

如上述，改變橫向位移相位Δ之值，可改變3D影像合成之結構。藉此，可達到改變最佳視點位置之目的。對於雙視景3D合成影像Σ_n(Δ=1)～Σ_n(Δ=6)，透過如圖19所示之雙視景用傾斜條狀視差光柵之作用後，相較於原Δ=0時之所有最佳視點P_k,i,j(x_c,y_c,Z₀)之位置，當Δ≠0時，所有P_k,i,j(x_c,y_c,Z₀)同時向左水平位移一Δx_c，成為移動後之最佳視點P’_k,i,j(x’_c,y_c,Z₀)。以下，稱P_k,i,j(x_c,y_c,Z₀)為主最佳視點；而稱主P’_k,i,j(x’_c,y_c,Z₀)為次最佳視點。如圖38～43所示，x’_c可如下式表示：As described above, changing the value of the lateral displacement phase Δ can change the structure of the 3D image synthesis. Thereby, the purpose of changing the optimal viewpoint position can be achieved. For the dual-view 3D synthetic image Σ_n (Δ=1) ～ Σ_n (Δ=6), after passing through the action of the oblique strip-shaped parallax barrier for the dual view as shown in FIG. 19, compared with the original Δ=0 At the time of all the best viewpoints P_k,i,j (x_c ,y_c ,Z₀ ), when Δ≠0, all P_k,i,j (x_c ,y_c ,Z₀ ) are simultaneously The left horizontal displacement is Δx_c , which becomes the best viewpoint P'_k,i,j (x'_c , y_c , Z₀ ) after the movement. Hereinafter, P_k,i,j (x_c ,y_c ,Z₀ ) is the main best viewpoint; and the main P'_k,i,j (x'_c ,y_c ,Z₀ ) is the second best. Viewpoint. As shown in Figures 38-43, x'_c can be expressed as follows:

x’_c=x_c-Δ x_c　(44)x'_c =x_c -Δ x_c (44)

其中，among them,

Δ x_c=Δ×L_E/m　(45)Δ x_c =Δ×L_E /m (45)

Δ x_c即為最佳視點可調變間距。當Δ=1時，可令Δ x_c0為最佳視點可調變最小間距，如下式：。Δ x_{c is} the optimum viewpoint adjustable pitch. When Δ=1, Δ x_c0 can be adjusted to the optimal viewpoint and the minimum spacing, as follows:

Δ x_c0=L_E/m　(46)Δ x_c0 =L_E /m (46)

是以，m越大(上述之圖示例，使用m=3)，可取得越小的Δx_c0。另外，由於視分離景裝置係為一線性之光學系統，是以，對於容許觀賞區341中之中心線Y_i,j(x,y)、邊界線Y_i,j⁺(x,y)、Y_i,j^-(x,y)，如圖44所示(圖例係使用Δ=0)，可透過改變Δ之值，皆向左做同一Δ x_c量之位移，如圖45所示(圖示例係使用Δ=1)，使得移動後之中心線、邊界線各自成為Y’_i,j(x,y)、Y’_i,j⁺(x,y)、Y’_i,j^-(x,y)。亦即，改變Δ之值，可讓所有的容許觀賞區341、與鬼影區342，同時做一向左之水平位移(當Δ>0)、或向右之水平位移(當Δ<0)。以下，稱Y_i,j(x,y)為主中心線；而稱Y’_i,j(x,y)為次中心線。Therefore, the larger m (the above example of the figure, m = 3), the smaller Δx_c0 can be obtained. In addition, since the view separating device is a linear optical system, the center line Y_i,j (x,y), the boundary line Y_i,j⁺ (x,y) in the allowable viewing area 341, Y_i,j^- (x,y), as shown in Figure 44 (the legend uses Δ = 0), can change the value of Δ, and do the same Δ x_c displacement to the left, as shown in Figure 45 ( The figure example uses Δ=1) so that the center line and the boundary line after the movement become Y'_i,j (x,y), Y'_i,j⁺ (x,y), Y'_i,j^- (x, y). That is, changing the value of Δ allows all of the allowable viewing area 341 and the ghosting area 342 to simultaneously perform a horizontal displacement (when Δ>0) or a horizontal shift to the right (when Δ<0). Hereinafter, Y_i,j (x,y) is referred to as the centerline; and Y'_i,j (x,y) is referred to as the secondary centerline.

如圖46所示，再將Δ=0與Δ=1之圖示做一重疊，以便觀察Δ改變前後，容許觀賞區位移之變化與重疊之狀況。根據式(16)，可計算取得容許觀賞區341之寬度ΔX_VF(圖示例係使用R_x=0.5)；根據式(46)，可計算取得主最佳視點可調變最小間距Δx_c0(圖示例係使用m=3)，當下式條件成立時：As shown in Fig. 46, the graphs of Δ=0 and Δ=1 are overlapped to observe the change and overlap of the viewing zone displacement before and after the Δ change. According to the formula (16), the width ΔX_{VF of the} allowable viewing area 341 can be calculated (the example is R_x = 0.5); according to the formula (46), the minimum optimal pitch Δx_c0 can be calculated and obtained ( The figure example uses m=3) when the following condition is true:

ΔX_VF>Δx_c0　(47)ΔX_VF >Δx_c0 (47)

即可讓Δ改變前後之容許觀賞區，產生重疊之現象。該重疊區345之寬度ΔX_OL，係可如下式表示：It is possible to make the Δ change before and after the allowable viewing area, resulting in overlapping phenomena. The width ΔX_{OL of} the overlap region 345 can be expressed as follows:

ΔX_OL=ΔX_VF-Δx_c0　(48)ΔX_OL = ΔX_{VF -} Δx_c0 (48)

將式(16)、(46)代入式(48)，可得：Substituting equations (16) and (46) into equation (48) yields:

ΔX_OL=(R_x-1/m)×L_E　(49)ΔX_OL = (R_x -1/m) × L_E (49)

令式(49)大於零，即成為觀賞自由度最佳化之方法，亦即，令R_x>1/m，即可達到於最佳觀賞面上構建無鬼影區之目的。If the formula (49) is greater than zero, it becomes the method of optimizing the viewing degree of freedom, that is, let R_x >1/m, the object can be constructed on the best viewing surface without ghosting.

對於位於最佳觀賞面之觀賞者，雖然，當其觀賞位置不恰當、或改變其觀賞位置時，可能造成觀看到鬼影或假立體影像之現象，但只要能即時檢測出觀賞者左右眼之水平位置，即可透過Δ之操作，將正確之容許觀賞區，移動至觀賞者雙眼所在之位置，即可達到完全解決鬼影與假立體影像之現象，並解除觀賞自由度不足之問題。For the viewers who are located on the best viewing surface, although the viewing position is inappropriate or the viewing position is changed, it may cause ghosting or fake stereoscopic images, but as long as the viewer’s left and right eyes can be detected immediately In the horizontal position, the correct allowable viewing area can be moved to the position of the viewer's eyes through the operation of Δ, and the phenomenon of ghosting and false stereoscopic images can be completely solved, and the problem of insufficient viewing freedom can be removed.

4.觀賞位置即時檢測之方法4. Method of instant detection of viewing position

如前述，觀賞位置係指左右眼所在之三次元位置(螢幕座標系)。如中華民國專利申請案號：096108692專利所揭示之一種視空間點認知之裝置，藉由一立體攝影之技藝，使用一對左、右攝影裝置，透過攝影、影像處理，從左、右攝影裝置所取出之2D影像中，以檢測出左、右眼球之(或者是瞳孔)中心位置(以上為數位相機習用之技術)，再利用一左右影像對應與三次元座標轉換計算之方法，可取得左、右眼三次元之位置。以下，只針對左右影像對應之方法與三次元座標轉換計算之方法，做一說明。As mentioned above, the viewing position refers to the three-dimensional position (screen coordinate system) where the left and right eyes are located. A device for visual spatial point recognition disclosed in the Patent Application No. 096108692, which uses a pair of left and right photographic devices to perform photography and image processing from left and right photographic devices by a stereoscopic photography technique. In the 2D image taken out, the center position of the left and right eyeballs (or the pupil) is detected (the above is a technique used by the digital camera), and the left and right image corresponding to the three-dimensional coordinate conversion calculation method can be used to obtain the left The position of the right eye three yuan. In the following, only the method corresponding to the left and right images and the method of calculating the ternary coordinate conversion are described.

首先，說明該立體攝影構成之光學特徵。如圖47～48所示，該立體攝影裝置23係由一左攝影裝置20、與一右攝影裝置21所構成，其裝置之方式，如圖49所示，係可以內藏之方式，直接裝置於一般平面顯示器螢幕框架24之內(如左圖)、或者是以外掛之方式，裝置於一般平面顯示器螢幕框架24之外(如右圖)。是以，該左右攝影機20、21，亦可以內藏、或外掛之方式，裝置於行動電話、數位相機、攝影機、遊戲機、平板點腦、筆記型電腦、監視器、電視、3D電視等裝置之機殼之上。First, the optical characteristics of the stereoscopic photographing will be described. As shown in FIGS. 47 to 48, the stereo camera 23 is composed of a left photographing device 20 and a right photographing device 21, and the device is arranged as shown in FIG. The device is mounted outside the general flat display screen frame 24 (as shown in the right figure) within the general flat display screen frame 24 (as shown in the left) or in an external manner. Therefore, the left and right cameras 20, 21 can also be built in, or plugged in, installed in a mobile phone, a digital camera, a video camera, a game machine, a tablet brain, a notebook computer, a monitor, a television, a 3D television, and the like. Above the case.

另外，對於該左、右攝影裝置20、21，令其具有相同之光學成像系統，即具有相同焦距f之光學成像透鏡(未圖示)、與相同之影像感應器(如CCD或CMOS，未圖示)。於該左、右攝影裝置20、21上，個別設置一左影像座標系X_LY_LZ_L、一右影像座標系X_RY_RZ_R。令該兩影像座標系之原點，係個別設置於該左、右攝影裝置20、21影像感應器之中心，且該兩影像座標系與螢幕座標系之座標軸，具有平行之關係。於螢幕座標系下，令該兩影像座標系之原點座標，係個別為(-S/2,H,0)、(S/2,H,0)。其中，S為該左、右攝影裝置20、21光軸間距，H則為裝置高度。另外，令Z_L、Z_R係個別設置於該左、右攝影裝置20、21光軸上。亦即，該左、右攝影裝置20、21之光軸，係平行於Z軸。In addition, for the left and right photographic devices 20, 21, they have the same optical imaging system, that is, an optical imaging lens (not shown) having the same focal length f, and the same image sensor (such as CCD or CMOS, not Graphic). A left image coordinate system X_L Y_L Z_L and a right image coordinate system X_R Y_R Z_{R are} separately disposed on the left and right photographing devices 20 and 21. The origins of the two image coordinate systems are individually set in the center of the left and right imaging devices 20 and 21, and the two image coordinate systems have a parallel relationship with the coordinate axes of the screen coordinate system. Under the screen coordinate system, the origin coordinates of the two image coordinate systems are (-S/2, H, 0), (S/2, H, 0). Where S is the optical axis spacing of the left and right imaging devices 20, 21, and H is the device height. Further, Z_L and Z_R are individually provided on the optical axes of the left and right imaging devices 20 and 21. That is, the optical axes of the left and right imaging devices 20, 21 are parallel to the Z axis.

如圖48所示，該左、右攝影裝置20、21成像之光學特徵，對於位於螢幕座標系中之一物點P(X_P,Y_P,Z_P)，經左、右攝影機光學成像系統之作用，會於左、右影像感測器上，即於左、右影像座標系上，各自產生一像點I_L(x_L,y_L,0)、I_R(x_R,y_R,0)。令I_L(x_L,y_L,0)、I_R(x_R,y_R,0)為P(X_P,Y_P,Z_P)之對應點，且具有以下座標轉換之關係：As shown in Fig. 48, the optical features of the left and right photographic devices 20, 21 are imaged by a left and right camera optical imaging system for an object point P (X_P , Y_P , Z_P ) located in the screen coordinate system. The role will be on the left and right image sensors, that is, on the left and right image coordinate systems, each generating an image point I_L (x_L , y_L , 0), I_R (x_R , y_R , 0). Let I_L (x_L , y_L , 0), I_R (x_R , y_R , 0) be the corresponding points of P(X_P , Y_P , Z_P ) and have the following coordinate transformation relationship:

是以，可將式(50)～(52)用於觀賞位置之檢測。對於位於螢幕座標系XYZ中之左、右眼10、11，其三次元之座標，係可如下定義：Therefore, the equations (50) to (52) can be used for the detection of the viewing position. For the left and right eyes 10, 11 located in the screen coordinate system XYZ, the coordinates of the three elements can be defined as follows:

E_L=(X_L,Y_L,Z_L)　(53)E_L = (X_L , Y_L , Z_L ) (53)

E_R=(X_R,Y_R,Z_R)　(54)E_R =(X_R ,Y_R ,Z_R ) (54)

該左、右眼10、11，經過該左、右攝影裝置20、21之光學透鏡，可個別成像於該左、右影像感應器，再經過影像處理，可個別檢測出左、右眼球(或者是瞳孔)中心之位置，如下表示：The left and right eyes 10 and 11 pass through the optical lenses of the left and right imaging devices 20 and 21, and can be individually imaged on the left and right image sensors, and then subjected to image processing to individually detect the left and right eyeballs (or Is the position of the center of the pupil, as follows:

左影像座標系中，左、右眼球(或者是瞳孔)中心之位置，可如下式表示：In the left image coordinate system, the position of the center of the left and right eyeballs (or pupils) can be expressed as follows:

i_L,L=(x_L,L,y_L,L,0)　(55)i_L,L =(x_L,L ,y_L,L ,0) (55)

i_L,R=(x_L,R,y_L,R,0)　(56)i_L,R =(x_L,R ,y_L,R ,0) (56)

右影像座標系中，左、右眼球(或者是瞳孔)中心之位置，可如下式表示：In the right image coordinate system, the position of the center of the left and right eyeballs (or the pupil) can be expressed as follows:

i_R,L=(x_R,L,y_R,L,0)　(57)i_R,L =(x_R,L ,y_R,L ,0) (57)

i_R,R=(x_R,R,y_R,R,0)　(58)i_R,R =(x_R,R ,y_R,R ,0) (58)

是以，上述之左右影像對應之方法，係指對左、右攝影裝置20、21影像感應器上之左右眼球中心位置，作一對應之處理。亦即，左眼位置E_L係由i_L,L與i_R,L所對應；而右眼位置E_R則由i_L,R與i_R,R所對應。另外，如前述，因該左、右攝影裝置20、21具有同樣光學特徵，可令y_L,L=y_R,L=y_L、且y_L,R=y_R,R=y_R。Therefore, the method corresponding to the left and right images described above refers to the processing of the center positions of the left and right eyeballs on the left and right imaging devices 20 and 21 of the image sensor. That is, the left eye position E_L is corresponding to i_{L, L} and i_{R, L} ; and the right eye position E_R is corresponding to i_{L, R} and i_{R, R.} Further, as described above, since the left and right photographing devices 20, 21 have the same optical characteristics, y_{L, L} = y_{R, L} = y_L , and y_{L, R} = y_{R, R} = y_{R can be obtained} .

是以，左眼球(或者是瞳孔)中心，對應於左、右影像座標系上之位置，可如下式表示：Therefore, the center of the left eyeball (or the pupil) corresponds to the position on the left and right image coordinate systems, and can be expressed as follows:

i_L,L=(x_L,L,y_L,0)　(59)i_L,L =(x_L,L ,y_L ,0) (59)

i_R,L=(x_R,L,y_L,0)　(60)i_R,L =(x_R,L ,y_L ,0) (60)

右眼球(或者是瞳孔)中心，對應於左、右影像座標系上之位置，可如下式表示：The center of the right eyeball (or pupil) corresponds to the position on the left and right image coordinate systems and can be expressed as follows:

i_L,R：(x_L,R,y_R,0)　(61)i_L,R :(x_L,R ,y_R ,0) (61)

i_R,R：(x_R,R,y_R,0)　(62)i_R,R :(x_R,R ,y_R ,0) (62)

所謂”三次元座標轉換計算之方法”，係透過一影像座標系與螢幕座標系間之座標轉換，將成像於影像座標係上，左、右眼之座標，轉換成影像座標係上之三次元座標。如上述，根據式(50)～(52)，對i_L,L、i_R,L作座標轉換，可計算取得左眼10三次元之座標，即式(53)中之各座標，可如下式表示：The so-called "three-dimensional coordinate conversion calculation method" is a coordinate conversion between an image coordinate system and a screen coordinate system, and is imaged on the image coordinate system, and the coordinates of the left and right eyes are converted into three-dimensional elements on the image coordinate system. coordinate. As described above, according to the equations (50) to (52), i_{L, L} , i_{R, L are} coordinate-converted, and the coordinates of the three-dimensional element of the left eye 10, that is, the coordinates in the equation (53) can be calculated, as follows: Expression:

同樣地，根據式(50)～(52)，對i_L,R、i_R,R作座標轉換，可計算取得右眼11三次元之座標，即式(54)中之各座標，可如下式表示：Similarly, according to the equations (50)-(52), i_{L, R} , i_{R, R are} coordinate-converted, and the coordinates of the three-dimensional element of the right eye 11 can be calculated, that is, the coordinates in the equation (54) can be as follows Expression:

5.觀賞條件最佳化之方法5. Method of optimizing viewing conditions

由於，視差光柵裝置具有觀賞自由度限制之光學特徵，需藉由以下觀賞距離、與正視螢幕等最佳化條件之設定，方可達到呈現最高3D影像品質之目的：Since the parallax barrier device has optical characteristics that limit the degree of freedom of viewing, it is necessary to set the optimal viewing conditions such as the viewing distance and the front view screen to achieve the highest 3D image quality:

(1)觀賞距離最佳化之條件(1) Conditions for viewing distance optimization

|Z_L-Z₀|＜ΔZ₀　(69)|Z_L -Z₀ |<ΔZ₀ (69)

︱Z_R-Z₀│<ΔZ₀　(70)—Z_R -Z₀ │<ΔZ₀ (70)

其中，ΔZ₀為可容許最佳觀賞距離之偏差量。式(69)～(70)所設定之條件，如圖50所示，係當檢測出觀賞者偏離最佳觀賞位置、且超出該預設範圍ΔZ₀時，可發出一警告訊息，以要求觀賞者雙眼之位置，需移至最佳觀賞距離Z₀。Where ΔZ₀ is the amount of deviation that can tolerate the best viewing distance. The conditions set by the equations (69) to (70) are as shown in FIG. 50, and when the viewer is detected to deviate from the optimal viewing position and exceeds the preset range ΔZ₀ , a warning message may be issued to request viewing. The position of both eyes needs to be moved to the best viewing distance Z₀ .

(2)正視螢幕最佳化之條件(2) Facing the conditions of screen optimizationa.排除觀賞者偏頭側視3D影像a. Exclude the viewer from looking at the 3D image

其中，Δφ為可容許水平觀賞角度之偏差量、為x軸之單位向量、E_R、E_L可視為座標向量。式(71)所設定之條件，如圖51所示，係當檢測出觀賞者之視線係向左、或向右偏離螢幕、且該偏向角度係超出一預設角度Δφ時，可發出一警告訊息，以要求觀賞者需更正視線，以正視螢幕。Where Δφ is the amount of deviation of the allowable horizontal viewing angle, The unit vector for the x-axis, E_R , E_L can be regarded as a coordinate vector. The condition set by the equation (71), as shown in FIG. 51, may issue a warning when it is detected that the viewer's line of sight is deviated to the left or right, and the deflection angle exceeds a predetermined angle Δφ. The message is to ask the viewer to correct the line of sight to face the screen.

b.排除觀賞者歪頭斜視3D影像b. Exclude viewers from squinting 3D images

其中，Δρ為可容許傾斜觀賞角度之偏差量。式(72)所設定之條件，如圖52所示，係當檢測出觀賞者歪著頭觀看影像、且該歪斜角度係大於預設角度Δρ時，可發出一警告訊息，以要求觀賞者需更正視線，以正視螢幕。Among them, Δρ is the amount of deviation of the allowable tilt viewing angle. The condition set by the formula (72) is as shown in FIG. 52, and when the viewer is detected to look at the image with the head tilted, and the skew angle is greater than the preset angle Δρ, a warning message may be issued to request the viewer to Correct the line of sight to face the screen.

是以，根據式(69)～(72)之條件，可令式(53)、(54)具有以下之關係：Therefore, according to the conditions of the equations (69) to (72), the equations (53) and (54) can be made to have the following relationship:

Y_L=Y_R=Y_E　(73)Y_L =Y_R =Y_E (73)

Z_L=Z_R=Z₀　(74)Z_L = Z_R = Z₀ (74)

是以，最終左、右眼之座標，即成為：E_L=(X_L,Y_E,Z₀)、E_R=(X_R,Y_E,Z₀)。亦即，式(73)、(74)係描述了觀賞者之最佳觀賞條件，當觀賞者之觀賞位置，係滿足(1)讓雙眼維持在同樣的最佳觀賞距離、(2)讓雙眼保持同樣之高度(即保持水平狀態)、(3)需讓雙眼正視螢幕等條件時，即可觀賞到具最佳品質之3D影像。Therefore, the coordinates of the final left and right eyes become: E_L = (X_L , Y_E , Z₀ ), E_R = (X_R , Y_E , Z₀ ). That is, the formulas (73) and (74) describe the best viewing conditions for the viewer. When the viewer's viewing position is satisfied, (1) the eyes are maintained at the same optimal viewing distance, (2) let When the eyes are kept at the same height (ie, kept at a level), and (3) the eyes are required to face the screen, you can see the best quality 3D images.

6.觀賞位置與視景最佳對位之方法6. The method of viewing the best alignment between position and view

如上述，所謂”觀賞位置與視景最佳對位”，係指根據式(63)～(68)所取得左、右眼之位置E_L、E_R、以及根據式(73)～(74)所示之最佳觀賞條件，透過一左右眼之特徵座標之計算、一最佳觀賞線上最佳視點座標之計算、並利用一視點與視景對位之程序，以計算取得適當之Δ後，再將正確之容許觀賞區，移動至觀賞者雙眼所在之位置，達到大幅提高3D影像品質與使用方便性之目的。As described above, the "optimal alignment between the viewing position and the visual view" means the positions E_L and E_{R of the} left and right eyes obtained according to the equations (63) to (68), and the equations (73) to (74). The best viewing conditions shown, through the calculation of the coordinates of the left and right eyes, the calculation of the best viewpoint coordinates on the best viewing line, and the use of a point-of-view and view alignment procedure to calculate the appropriate Δ Then, the correct allowable viewing area can be moved to the position where the viewer's eyes are located, thereby achieving the purpose of greatly improving the quality and ease of use of the 3D image.

首先，重新定義中心線，令Y_i,j,Δ(x,y)取代上述所有主中心線Y_i,j(x,y)、次中心線Y’_i,j(x,y)，用以界定畫分觀賞者左右眼可能存在之容許觀賞區。亦即，Y_i,j,Δ=0(x,y)為原定義之主中心線；Y_i,j,Δ≠0(x,y)則為原定義之次中心線。該中心線Y_i,j,Δ(x,y)，可如下表示：First, redefine the centerline, and let Y_i,j,Δ (x,y) replace all the main centerlines Y_i,j (x,y) and the secondary centerline Y'_i,j (x,y). To allow the viewing area to be visible to the left and right eyes of the viewer. That is, Y_i,j , Δ=0(x,y) is the main center line of the original definition; Y_i,j ,Δ≠0(x,y) is the sub-center line of the original definition. The center line Y_i,j , Δ(x,y) can be expressed as follows:

y=f(θ){x-[n×i-(n-1)/2+j-Δ/m]×L_E}　(75)y=f(θ){x-[n×i-(n-1)/2+j-Δ/m]×L_E } (75)

當y=0時，可得Y_i,j,Δ(x,y)與X軸交點之座標值x(i,j,Δ)：When y = 0, the coordinate value x(i, j, Δ) of the intersection of Y_{i, j} , Δ(x, y) and the X-axis is obtained:

x(i,j,Δ)=[n×i-(n-1)/2+j-Δ/m]×L_E　(76)x(i,j,Δ)=[n×i-(n-1)/2+j-Δ/m]×L_E (76)

其中，f(θ)、L_E、n(=2)、m(=3)、i、j，如前述之定義。如圖53所示，係將Δ=0、1、2代入式(75)，所得之Y_i,j,Δ(x,y)。是以，藉由Δ>0之操作，可達到將所有主中心線Y_i,j,0(x,y)做向左位移之目的。如圖54所示，係將Δ=-0、-1、-2代入式(75)，所得之Y_i,j,Δ(x,y)。是以，藉由Δ<0之操作，可達到將所有主中心線Y_i,j,0(x,y)做向右位移之目的。如圖55所示，係將Δ=0、1、2與Δ=-0、-1、-2代入式(76)，所計算取得Y_i,j,Δ(x,y)與X軸交點之座標值x(i,j,Δ)。不論Δ=0、1、2或Δ=-0、-1、-2，所得交點之座標值x(i,j,Δ)，係為一致。另外，根據前述，x(i,j,Δ=0)即為主最佳視點；而x(i,j,Δ≠0)則為次最佳視點。當Δ=±m(即±3)時，所有主中心線、主最佳視點，皆向左(Δ=m)或是皆向右(Δ=-m)移動一雙眼間距L_E之距離。以下，對於所有之x(i,j,Δ=0)與x(i,j,Δ≠0)，泛稱為最佳觀賞線上之最佳視點。Where f(θ), L_E , n(=2), m(=3), i, j are as defined above. As shown in Fig. 53, Δ = 0, 1, 2 are substituted into the formula (75), and Y_{i, j} , Δ (x, y) are obtained. Therefore, by the operation of Δ>0, the purpose of shifting all the main center lines Y_i,j ,0(x,y) to the left can be achieved. As shown in Fig. 54, Δ = -0, -1, -2 are substituted into the formula (75), and Y_{i, j} , Δ (x, y) are obtained. Therefore, by the operation of Δ<0, the purpose of shifting all the main center lines Y_i,j ,0(x,y) to the right can be achieved. As shown in Fig. 55, Δ = 0, 1, 2 and Δ = -0, -1, -2 are substituted into equation (76), and the intersection of Y_{i, j} , Δ(x, y) and the X-axis is calculated. The coordinate value x (i, j, Δ). Regardless of Δ=0, 1, 2 or Δ=-0, -1, -2, the coordinate values x(i, j, Δ) of the resulting intersections are identical. Further, according to the above, x(i, j, Δ = 0) is the main optimal viewpoint; and x (i, j, Δ ≠ 0) is the sub-optimal viewpoint. When Δ=±m (ie ±3), all main center lines and main best viewpoints are shifted to the left (Δ=m) or both to the right (Δ=-m) by a distance between two eye distances L_E . Hereinafter, for all x(i, j, Δ = 0) and x (i, j, Δ ≠ 0), it is generally referred to as the best viewpoint on the best viewing line.

如圖19所示，當左、右眼10、11之觀看位置，係各自置放於同一可視區內最佳視點之容許觀賞範圍321時，可觀賞到正確之三次元影像，但若偏離該位置，則進入鬼影區322、323。另外，左、右眼10、11之觀看位置，若置放於不同可視區內之最佳視點時，則可能碰到假立體、或者是鬼影現象之現象。這些現象，皆發生於相鄰兩主最佳視點間，是以，藉由|Δ|<m之操作，可達到完全解決鬼影與假立體之問題。As shown in FIG. 19, when the viewing positions of the left and right eyes 10, 11 are placed in the allowable viewing range 321 of the best viewpoint in the same viewing area, the correct three-dimensional image can be viewed, but if the deviation is The location then enters ghost areas 322, 323. In addition, if the viewing positions of the left and right eyes 10, 11 are placed in the best viewpoints in different viewing zones, the phenomenon of false stereo or ghosting may be encountered. These phenomena occur between the two adjacent best viewpoints. Therefore, by the operation of |Δ|<m, the problem of ghost and false stereo can be completely solved.

如圖56所示，對於主最佳視點x(i=0,j=0,Δ=0)(如左邊圖所示)，做|Δ|≦m之操作，以達到向左、或向右之位移操作之目的。亦即，將Δ=0、1、2、3(如中間圖所示)與Δ=-0、-1、-2、-3(如右邊圖所示)代入式(76)，所計算取得之主、次最佳視點。是以，當所檢測出左右眼之位置後，只要找出最接近之Y_i,j,Δ(x,y)，再藉由|Δ|≦m之操作，即可達到3D眼睛追蹤之目的。As shown in Fig. 56, for the main best viewpoint x (i = 0, j = 0, Δ = 0) (as shown in the left figure), the operation of |Δ|≦m is performed to reach left or right. The purpose of the displacement operation. That is, Δ = 0, 1, 2, 3 (as shown in the middle figure) and Δ = -0, -1, -2, -3 (as shown in the right figure) are substituted into equation (76), which is calculated. The main and sub-optimal viewpoints. Therefore, when the position of the left and right eyes is detected, the closest Y_{i, j, Δ} (x, y) can be found, and then the operation of |Δ|≦m can achieve the purpose of 3D eye tracking. .

該觀賞位置與視景最佳對位之方法，係對於已具有最佳觀賞條件之雙眼位置，根據前述容許觀賞範圍之中心線與邊界線，首先，找出所左右眼所個別對應之可視區之編號i、最接近之視景編號j、與最接近之橫向位移相位Δ，實際之實施方法，如下述。The method for optimally aligning the viewing position with the viewing view is for the binocular position that has the best viewing condition, and according to the center line and the boundary line of the allowable viewing range, firstly, the individual corresponding to the left and right eyes is visually located. The area number i, the closest view number j, and the closest lateral displacement phase Δ, the actual implementation method, as described below.

如圖57所示，首先，令具有同樣傾斜角度θ之斜線L_L、L_R，個別通過該左右眼之位置(X_L,Y_L,Z_L)、(X_R,Y_R,Z_R)，並與X軸個別交會於x_L0、x_R0。以下對於x_L0、x_R0，稱之為左右眼之特徵座標。對於具右傾斜結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：As shown in Fig. 57, first, the oblique lines L_L and L_R having the same inclination angle θ are individually passed through the positions of the left and right eyes (X_L , Y_L , Z_L ), (X_R , Y_R , Z_R ). And intersect with the X axis in x_L0 , x_R0 . The following is the characteristic coordinates of the left and right eyes for x_L0 and x_R0 . For a parallax barrier device with a right-inclined structure, the x_L0 and x_R0 are calculated as follows:

x_L0=X_L+tan(θ)×Y_L　(77)x_L0 =X_L +tan(θ)×Y_L (77)

x_R0=X_R+tan(θ)×Y_R　(78)x_R0 =X_R +tan(θ)×Y_R (78)

對於具左傾斜結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：For a parallax barrier device with a left-inclined structure, the x_L0 and x_R0 are calculated as follows:

x_L0=X_L-tan(θ)×Y_L　(79)x_L0 =X_L -tan(θ)×Y_L (79)

x_R0=X_R-tan(θ)×Y_R　(80)x_R0 =X_R -tan(θ)×Y_R (80)

對於垂直結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：For a parallax barrier device of vertical structure, the x_L0 and x_R0 are calculated as follows:

x_L0=X_L　(81)x_L0 =X_L (81)

x_R0=X_R　(82)x_R0 =X_R (82)

是以，根據式(77)～(82)計算所得之左右眼之特徵座標x_L0、x_R0，與式(76)計算所得最佳觀賞線上之最佳視點x(i,j,Δ)做一比對，即可找出最接近之i,j,Δ值。藉由Δ之操作，可達3D眼睛追蹤之目的。以下，說明實際處理程序，並稱該程序為”視點與視景對位之程序”。Therefore, the characteristic coordinates x_L0 and x_R0 of the left and right eyes calculated according to the equations (77) to (82) are compared with the optimal viewpoint x(i, j, Δ) calculated on the best viewing line calculated by the equation (76). A comparison can find the closest i, j, Δ value. With the operation of Δ, the purpose of 3D eye tracking can be achieved. Hereinafter, the actual processing procedure will be described, and the program will be referred to as "a program of the viewpoint and the view alignment".

首先，補充定義”最佳可視面(Optimum Viewable Plane)”、水平可視角(Horizontal Viewable Angle)、與垂直可視角(Vertical Viewable Angle)。如圖58所示，所謂”最佳可視面”，係指於該最佳觀賞面上，存在一面積為有限之可視面350，於該面上只存在數量為有限之多數個最佳視點P_k,i,j，該多數個最佳視點P_k,i,j，係可對於左右眼，各自提供一具有低鬼影、與影像亮度接近之單一視景影像。該有限數量之最佳視點P_k,i,j所構成之面，即為最佳可視面。對於存在於該最佳觀賞面350上之任一點座標(x,y,Z₀)，具有以下之關係：First, the definitions are "Optimum Viewable Plane", Horizontal Viewable Angle, and Vertical Viewable Angle. As shown in Fig. 58, the "best visible surface" means that there is a limited visible surface 350 on the optimal viewing surface, and only a limited number of optimal viewpoints P exist on the surface._{k, i, j} , the plurality of best viewpoints P_{k, i, j} , for each of the left and right eyes, each providing a single scene image having a low ghost and close to the brightness of the image. The face formed by the finite number of best viewpoints P_k,i,j is the best visible surface. For any point coordinates (x, y, Z₀ ) present on the optimal viewing surface 350, the following relationship is obtained:

-x_max≦x≦x_max　(83)-x_max ≦x≦x_max (83)

-y_max≦y≦y_max　(84)-y_max ≦y≦y_max (84)

其中，x_max、y_max即規範該最佳可視面之範圍。亦即，觀賞者可於式(83)、(84)所定義之範圍內，觀賞到最佳品質之3D影像。一般，係於最佳觀賞面上，透過對3D影像作實際之量測(如cross-talk與亮度量測)，以取得該x_max、y_max之值。另外，根據該x_max、y_max，可定義一水平可視角Ω_H、與垂直可視角Ω_V，並可如下式表示：Where x_max and y_max are the ranges in which the optimal visible surface is specified. That is, the viewer can view the best quality 3D image within the range defined by the formulas (83) and (84). Generally, it is based on the best viewing surface, and the actual measurement of the 3D image (such as cross-talk and brightness measurement) is performed to obtain the values of x_max and y_max . In addition, according to the x_max and y_max , a horizontal view angle Ω_H and a vertical view angle Ω_V may be defined and may be expressed as follows:

Ω_H=2×tan^-1(x_max/Z₀)　(85)Ω_H = 2 × tan^-1 (x_max /Z₀ ) (85)

Ω_V=2×tan^-1(y_max/Z₀)　(86)Ω_V = 2 × tan^-1 (y_max /Z₀ ) (86)

當然，該x_max、y_max之值，亦可各自對應一i_max、k_max，如圖59、60所示，使得存在於最佳可視面上之最佳可視點P_k,i,j，該P_k,i,j中之水平可視區編號i、垂直可視區編號k，係可具有以下之關係：Of course, the values of x_max and y_max may also correspond to an i_max , k_max , as shown in FIGS. 59 and 60 , so that the best visible point P_k,i,j exists on the optimal visible surface. The horizontal visible area number i and the vertical visible area number k in the P_{k, i, j} may have the following relationships:

|i|≦i_max　(87)|i|≦i_max (87)

|k|≦k_max　(88)|k|≦k_max (88)

另外，可令x_max與i_max、y_max與k_max、係具有以下之關係：In addition, x_max and i_max , y_max and k_max can be made to have the following relationship:

x_max=i_max×n×L_E　(89)x_max =i_max ×n×L_E (89)

y_max=k_max×L_V　(90)y_max =k_max ×L_V (90)

當觀賞者之觀賞視角，係滿足小於Ω_H、Ω_V時，可觀賞到高品質之3D影像。當觀賞視角變大、且超出該Ω_H、Ω_V時，由於視景分離裝置之加工與組裝誤差，會破壞前述所有線性光學之特徵，除了嚴重惡化鬼影之外，亦會造成左右眼影像亮度差異過大，以致造成3D影像品質低下，甚至造成3D影像無法觀賞之問題。以下，根據上述之定義、與假設觀賞者之觀賞觀賞條件與位置，係個別滿足前述式(69)～(74)、式(83)～(84)所定義之條件，對於上述之該視點與視景對位之程序，說明其實施步驟如下：如前述，由於x_L0、x_R0之間距，即為雙眼間距L_E，是以，只要針對左眼位置x_L0、或右眼位置x_R0，與x(i,j,Δ)做一比對，即可找出最佳之i,j,Δ。為簡化圖示與說明，以下，左眼位置x_L0為例，說明之。When the viewing angle of the viewer is less than Ω_H and Ω_V , high-quality 3D images can be viewed. When the viewing angle becomes larger and exceeds the Ω_H and Ω_V , the processing and assembly errors of the visor separating device may destroy all the characteristics of the linear optical, and may cause left and right eye images in addition to severely deteriorating ghosts. The difference in brightness is too large, resulting in poor 3D image quality and even the problem that 3D images cannot be viewed. Hereinafter, according to the above definition and the viewing condition and position of the viewer, the conditions defined by the above formulas (69) to (74) and (83) to (84) are individually satisfied, and the viewpoint and the above viewpoint are visual position of the program, indicating that the implementation steps are as follows: as described above, since_{the L0} x, x_R0 of the pitch, i.e. the interocular distance L_E, is, as long as_{the L0} x x position for the left eye, the right eye or the position_R0 , by comparing x(i, j, Δ), you can find the best i, j, Δ. In order to simplify the illustration and description, the left eye position x_{L0 is taken} as an example below.

步驟一、確認左右眼之位置(x_L,y_E,z₀)、(x_R,y_E,z₀)，是否存在於最佳可視面範圍之內。如果，滿足下式之關係，則跳至步驟二；若不滿足下式之關係，則宣告觀賞位置偏離最佳可視面範圍，跳至步驟五；；Step 1. Confirm whether the positions of the left and right eyes (x_L , y_E , z₀ ), (x_R , y_E , z₀ ) exist within the optimal visible surface range. If the relationship of the following formula is satisfied, skip to step 2; if the relationship of the following formula is not satisfied, declare the viewing position to deviate from the optimal visible surface range, and skip to step 5;

│x_L│≦x_max　(91)│x_L │≦x_max (91)

│x_R│≦x_max　(92)│x_R │≦x_max (92)

│y_E│≦y_max　(93)│y_E │≦y_max (93)

步驟二、設定起始值，如下式：Step 2: Set the starting value as follows:

i=-i_max　(94)i=-i_max (94)

j=0；　(95)j=0; (95)

步驟三、將i,j,Δ代入式(76)，計算x(i,j,Δ)Step 3. Substituting i, j, Δ into equation (76) and calculating x(i, j, Δ)

步驟四、比對x_L0與x(i,j,Δ)，如下式：Step 4:_Align x_L0 with x(i, j, Δ) as follows:

│x_L0-x(i,j,Δ)|≦L_E/2m　(96)│x_L0 -x(i,j,Δ)|≦L_E /2m (96)

情況1：若找到一組(i,j,Δ)參數，符合式(96)之關係，則將Δ代入式(3)、或(4)、並宣告3D眼睛追蹤成功，跳至步驟五；Case 1: If a set of (i, j, Δ) parameters is found, in accordance with the relationship of equation (96), then Δ is substituted into equation (3), or (4), and the 3D eye tracking is successful, and the process proceeds to step 5;

情況2：若找不到一組(i,j,Δ)參數，符合式(96)之關係，則令Case 2: If a set of (i, j, Δ) parameters are not found, in accordance with the relationship of equation (96), then

j=j+2　(97)j=j+2 (97)

若j<n(即j未超出i可視區)，則跳至步驟三；若j≧n(即j已超出i可視區)，則令If j<n (ie j does not exceed the i viewable area), skip to step 3; if j≧n (ie j has exceeded the i viewable area), then

i=i+1　(98)i=i+1 (98)

j=0；　(99)j=0; (99)

若i≦i_max，跳至步驟三；若i>i_max，宣告觀賞位置偏離可視角範圍，跳至步驟五；If i≦i_max , skip to step 3; if i>i_max , declare the viewing position to deviate from the viewable range, skip to step 5;

步驟五、結束比對Step 5, end the comparison

對於上述式(96)之比較運算，如圖61所示，係以前述雙視景顯示(n=2、m=3)、且以i=0、j=0之可視區為例，以進行x_L0與x(0,0,3)、x(0,0,2)、x(0,0,1)、x(0,0,0)、x(0,0,-1)、x(0,0,-2)、x(0,0,-3)之比對。是以，只要x_L0滿足x(0,0,3)-L_E/6≦x_L0≦x(0,0,-3)+L_E/6之條件時，即可找出對應之Δ值。如圖62所示，係以前述四視景顯示(n=4、m=3)、且以i=0、j=0與i=1、j=0之可視區為例，以進行x_L0之比較運算。如圖63所示，係以前述四視景顯示(n=4、m=3)、且以i=0、j=2之可視區為例，以進行x_L0之比較運算。For the comparison operation of the above formula (96), as shown in FIG. 61, the double-view display (n=2, m=3) and the visible area of i=0 and j=0 are taken as an example to perform x_L0 and x(0,0,3), x(0,0,2), x(0,0,1), x(0,0,0), x(0,0,-1),x Alignment of (0,0,-2), x(0,0,-3). Therefore, as long as x_L0 satisfies the condition of x(0,0,3)-L_E /6≦x_L0 ≦x(0,0,-3)+L_E /6, the corresponding Δ value can be found. . As shown in FIG. 62, the four-view display (n=4, m=3), and the visible area of i=0, j=0, i=1, j=0 are taken as an example to perform x_{L0 .} Comparison operation. As shown in FIG. 63, the four-view display (n=4, m=3) and the visible area of i=0 and j=2 are taken as an example to perform a comparison operation of x_L0 .

當然，該視點與視景對位之程序，亦可以右眼位置x_R0，進行比對之運算，但式(95)處j起始值，需令j=1；式(96)中，需以x_R0替代x_L0，如下式：Of course, the program of the viewpoint and the view alignment can also perform the comparison operation on the right eye position x_R0 , but the j start value at the formula (95) needs to be j=1; in the formula (96), Replace x_L0 with x_R0 as follows:

|x_R0-x(i_R,j_R,Δ)|<L_E/m　(100)|x_R0 -x(i_R ,j_R ,Δ)|<L_E /m (100)

當j已超出i視區，式(99)中之j，需令j=1。When j has exceeded the i viewport, j in equation (99), j = 1 is required.

如圖64所示，係本發明實施例之示意圖。本發明一種多視景三次元影像顯示之方法400，主要係由一觀賞位置即時檢測方法410、一觀賞位置與視景最佳對位之方法420、一動態多視景3D影像合成之方法430、一平面顯示器螢幕440、與一靜態視差光柵裝置450所構成。Figure 64 is a schematic view of an embodiment of the present invention. The method 400 for multi-view three-dimensional image display is mainly composed of an instant detection method 410 for viewing position, a method 420 for optimal viewing position and visual view, and a method for synthesizing dynamic multi-view 3D image 430. A flat display screen 440 is constructed with a static parallax barrier device 450.

該觀賞位置即時檢測方法410，如前述，主要係利用一對左、右攝影裝置412，透過攝影、影像處理，從左、右攝影裝置所取出之2D影像中，於左、右影像座標系係，以檢測出左、右眼球之(或者是瞳孔)中心位置(如式(55)～(58)所示)，再利用一左右影像對應之程序414(如式(59)～(61)所示)、一三次元座標轉換計算之程序416(如式(63)～(68)所示)、與一觀賞條件最佳化之程序418(如式(69)～(74)所示)，可取得及輸出一左、右眼三次元之位置E_L=(X_L,Y_E,Z₀)、E_R=(X_R,Y_E,Z₀)。The viewing position real-time detecting method 410, as described above, mainly uses a pair of left and right photographing devices 412, through the photographing and image processing, and the left and right image coordinate systems in the 2D images taken out from the left and right photographing devices. To detect the center position of the left and right eyeballs (or the pupils) (as shown in equations (55) to (58)), and then use a program 414 corresponding to the left and right images (such as equations (59) to (61). a program 416 (as shown in equations (63) to (68)) for calculating a three-dimensional coordinate conversion calculation, and a program 418 for optimizing an ornamental condition (as shown in equations (69) to (74)) , can obtain and output a left and right eye three-dimensional position E_L = (X_L , Y_E , Z₀ ), E_R = (X_R , Y_E , Z₀ ).

該觀賞位置與視景最佳對位之方法420，如前述，主要係根據該左、右眼三次元位置E_L、E_R，透過一左右眼之特徵座標計算之程序422(如式(77)～(82)所示)、一最佳觀賞線上最佳視點座標計算之程序424(如式(76)所示)、與一視點與視景對位之程序426，以計算取得及輸出一適當之Δ。The method 420 for optimally aligning the viewing position with the visual view, as described above, is mainly based on the left and right eye three-dimensional positions E_L , E_R , and the program 422 calculated by the feature coordinates of one of the left and right eyes (eg, equation (77) ～(82)), a program 424 for calculating the best viewpoint coordinates on the best viewing line (as shown in equation (76)), and a program 426 for aligning with a viewpoint and a view to calculate and output one Appropriate Δ.

該動態多視景3D影像合成之方法430，如前述，主要係對於一多視景影像432(如式(1)所示)，根據Δ與一多視景3D影像合成之程序432(如式(42)～(43)所示)，以產生一多視景3D合成影像Σ_n。The method 430 for dynamic multi-view 3D image synthesis, as described above, is mainly for a multi-view image 432 (as shown in equation (1)), according to a program 432 for synthesizing Δ with a multi-view 3D image (eg, (42) to (43)) to generate a multi-view 3D composite image Σ_n .

該平面顯示器螢幕440，如前述，主要係接收與顯示該多視景3D合成影像Σ_n。The flat display screen 440, as described above, primarily receives and displays the multi-view 3D composite image Σ_n .

該靜態視差光柵裝置450，如前述，對於該多視景3D合成影像Σ_n，可於最佳觀賞距離上，提供一最佳觀賞面，並於該最佳觀賞面上，提供多數個最佳視點，可於該最佳視點處，作視景分離之光學作用，達到個別呈現單一視景影像之目的；另外，對於該視差光柵之光學結構，主要係利用一靜態視差光柵裝置設計之方法452(如式(6)～(17)與式(23)～(31)所示)、與一觀賞自由度最佳化之方法454(如式(47)、(49)所示)，達到最佳化設計之目的。是以，可於一最佳可視面上，將該多視景3D合成影像Σ_n(t)，作視景分離之作用、並將正確之左右影像，投射至觀賞者之左右眼10、11，達到三次元影像顯示之目的The static parallax barrier device 450, as described above, provides an optimal viewing surface for the optimal viewing distance for the multi-view 3D composite image ,_n , and provides most optimal images on the optimal viewing surface. The viewpoint can be used as the optical effect of the separation of the vision at the optimal viewpoint to achieve the purpose of individually presenting a single scene image. In addition, for the optical structure of the parallax barrier, the method of designing a static parallax barrier device is mainly used. (as shown in equations (6) to (17) and equations (23) to (31)), and a method 454 for optimizing the degree of freedom of viewing (as shown in equations (47) and (49)), reaching the maximum The purpose of the design. Therefore, the multi-view 3D synthetic image Σ_n (t) can be used as a visual separation on an optimal visible surface, and the correct left and right images are projected to the left and right eyes of the viewer 10 and 11 , to achieve the purpose of three-dimensional image display

以上所述之”程序”，係指一可處理本發明中所有相關公式計算之軟體程式，並可透過一般之微處理器、或DSP等計算裝置，可執行該軟體程式。The above-mentioned "program" refers to a software program that can process all relevant formula calculations in the present invention, and can execute the software program through a general microprocessor, or a computing device such as a DSP.

綜上所述，本發明為一種三次元影像顯示之方法，主要係對於利用一般平面顯示器螢幕與靜態視差光柵裝置以顯示三次元影像時，本發明提出(1)一靜態視差光柵裝置設計之方法、(2)一動態多視景3D影像合成之方法、(3)一觀賞自由度最佳化之方法、(4)一觀賞位置即時檢測方法、(5)一觀賞條件最佳化之方法與(6)一觀賞位置與視景最佳對位方法，可於最佳可視面上，有效解決鬼影、假立體影像、與水平與垂直方向觀賞自由度不足之問題，達到大幅提高3D影像品質與使用方便性之目的。In summary, the present invention is a three-dimensional image display method, mainly for the use of a general flat display screen and a static parallax barrier device to display a three-dimensional image, the present invention proposes (1) a static parallax barrier device design method (2) a method for dynamic multi-view 3D image synthesis, (3) a method for optimizing viewing degree of freedom, (4) an instant detection method for viewing position, and (5) a method for optimizing viewing conditions and (6) An optimal alignment method between viewing position and visual view can effectively solve the problem of ghosts, fake stereoscopic images, and insufficient degree of freedom of viewing in horizontal and vertical directions on the best visible surface, thereby greatly improving the quality of 3D images. For the purpose of ease of use.

以上所述者，僅為本發明之較佳實施例而已，當不能以之限定本發明所實施之範圍，即大凡依本發明申請專利範圍所作之均等變化與修飾，皆應仍屬於本發明專利涵蓋之範圍內。另外，對於本發明所開示之各方法，尤其是(2)動態多視景3D影像合成之方法、(4)觀賞位置即時檢測方法、與(5)觀賞位置與視景最佳對位方法，亦適用於其他靜態視景分離裝置(如柱狀透鏡陣列)、動態視景分離裝置。謹請貴審查委員明鑑，並祈惠准，是所至禱。The above is only the preferred embodiment of the present invention, and the scope of the present invention is not limited thereto, that is, the equivalent variations and modifications made by the scope of the present invention should still belong to the present invention. Within the scope of coverage. In addition, for the methods disclosed in the present invention, in particular, (2) a method for dynamic multi-view 3D image synthesis, (4) an instant detection method for viewing position, and (5) an optimal alignment method for viewing position and visual view, It is also applicable to other static view separation devices (such as lenticular lens arrays) and dynamic view separation devices. I would like to ask your review board member to give a clear explanation and pray for it. It is the prayer.

1．．．平面顯示器螢幕1. . . Flat panel display

2．．．各次畫素間之黑色間隔2. . . Black interval between each pixel

3．．．裸眼視三次元影像顯示器螢幕3. . . Naked eye three-dimensional image display screen

10．．．左眼10. . . Left eye

11．．．右眼11. . . Right eye

20．．．左攝影裝置20. . . Left camera

21．．．右攝影裝置twenty one. . . Right photographic device

23．．．立體攝影裝置twenty three. . . Stereoscopic device

24．．．平面顯示器螢幕框架twenty four. . . Flat display screen frame

310．．．雙視景用傾斜條狀視差光柵310. . . Inclined strip-shaped parallax barrier for dual view

311．．．傾斜條狀透光元件311. . . Tilt strip light transmitting element

312．．．傾斜條狀遮蔽元件312. . . Tilt strip shielding element

321．．．水平容許觀賞範圍321. . . Horizontal allowable viewing range

322、323．．．水平鬼影區322, 323. . . Horizontal ghost area

331．．．垂直容許觀賞範圍331. . . Vertical allowable viewing range

332．．．垂直鬼影區332. . . Vertical ghost area

341．．．傾斜帶狀之容許觀賞範圍341. . . Inclined band shape

342．．．傾斜帶狀之鬼影區342. . . Tilted ribbon ghost area

345．．．容許觀賞區重疊之區域345. . . Allowing areas where the viewing area overlaps

350．．．最佳可視面350. . . Best visible surface

400．．．本發明之實施例400. . . Embodiment of the present invention

410．．．觀賞位置即時檢測方法410. . . Instant detection method for viewing position

412．．．一對左、右攝影裝置412. . . a pair of left and right photographic devices

414．．．左右影像對應之程序414. . . Program corresponding to left and right images

416．．．三次元座標轉換計算之程序416. . . Three-dimensional coordinate conversion calculation program

418．．．觀賞條件最佳化之程序418. . . Program for optimizing viewing conditions

420．．．觀賞位置與視景最佳對位之方法420. . . Method for viewing the best alignment between position and view

422．．．左右眼之特徵座標計算之程序422. . . Procedure for calculating the coordinates of the left and right eyes

424．．．最佳觀賞線上最佳視點座標計算之程序424. . . Best viewing line coordinates calculation program

426．．．視點與視景對位之程序426. . . Program for viewing point and view

430．．．動態多視景3D影像合成之方法430. . . Dynamic multi-view 3D image synthesis method

432．．．多視景影像432. . . Multi-view image

434．．．多視景3D影像合成之程序434. . . Multi-view 3D image synthesis program

440．．．平面顯示器螢幕440. . . Flat panel display

450．．．靜態視差光柵裝置450. . . Static parallax barrier device

452．．．靜態視差光柵裝置設計之方法452. . . Method for designing static parallax barrier device

454．．．觀賞自由度最佳化之方法454. . . Method of optimizing viewing freedom

XYZ．．．螢幕座標系XYZ. . . Screen coordinate system

X、Y、Z．．．座標軸方向X, Y, Z. . . Coordinate axis direction

．．．x軸之單位向量 . . . Unit vector of x-axis

R．．．紅色R. . . red

G．．．綠色G. . . green

B．．．藍色B. . . blue

W．．．白色W. . . white

N．．．顯示器螢幕水平方向次畫素之總數N. . . The total number of sub-pixels in the horizontal direction of the display screen

M．．．顯示器螢幕垂直方向次畫素之總數M. . . The total number of sub-pixels in the vertical direction of the display screen

j、i．．．單一個次畫素之水平與垂直位置編號j, i. . . Horizontal and vertical position number of a single pixel

P_H．．．次畫素之水平寬度P_H . . . Horizontal width of secondary pixels

P_V．．．次畫素之垂直高度P_V . . . Vertical height of the secondary pixel

H×V．．．單一個次畫素有效發光尺寸H×V. . . Single sub-pixel effective light size

V_k．．．單一視景影像V_k . . . Single view image

k、Λ、0、1、2、3．．．視景編號數k, Λ, 0, 1, 2, 3. . . Sight number

．．．V_k影像中位於(i,j)位置之次畫素影像資料 . . . Subpixel image data at (i, j) position in V_k image

Σ_n．．．多視景3D合成影像Σ_n . . . Multi-view 3D composite image

Σ_n(t)．．．以時間為變數之多視景3D合成影像Σ_n (t). . . Multi-view 3D synthetic image with time as variable

n．．．總視景數n. . . Total number of views

m．．．橫向最小顯示單元次畫素構成之數目m. . . The number of sub-pixels in the horizontal minimum display unit

Q．．．縱向最小顯示單元次畫素構成之數目Q. . . Number of vertical minimum display unit sub-pixels

Δ．．．橫向位移相位Δ. . . Lateral displacement phase

Δ(t)．．．以時間為變數之橫向位移相位Δ(t). . . Lateral displacement phase with time as variable

t．．．時間t. . . time

Π．．．橫向位移振幅Hey. . . Lateral displacement amplitude

int．．．係取整數之函數Int. . . a function that takes an integer

Mod．．．取餘數之函數Mod. . . Function of remainder

B_H．．．透光元件之水平寬度B_H . . . Horizontal width of light transmitting element

．．．遮蔽元件之水平寬度 . . . Horizontal width of the shielding element

ΔB_H．．．透光元件開口水平寬度之縮減量ΔB_H . . . Reduced horizontal width of light-transmitting element opening

B_V．．．透光元件垂直開口寬度B_V . . . Vertical opening width of light transmitting element

ΔB_V．．．透光元件開口垂直寬度之縮減量ΔB_V . . . Reduced vertical width of the transparent element opening

ΔX_VF．．．水平容許觀賞範圍ΔX_VF . . . Horizontal allowable viewing range

ΔY_VF．．．垂直容許觀賞範圍ΔY_VF . . . Vertical allowable viewing range

R_x．．．水平觀賞自由度R_x . . . Horizontal viewing freedom

R_Y．．．垂直觀賞自由度R_Y . . . Vertical viewing freedom

θ．．．傾斜條狀視差光柵之傾斜角度θ. . . Inclination angle of oblique strip-shaped parallax barrier

Z₀．．．最佳觀賞距離Z₀ . . . Best viewing distance

L_B．．．傾斜條狀視差光柵之裝置距離L_B . . . Device distance of oblique strip-shaped parallax barrier

P_k,i,j(x_c,y_c,Z₀)．．．最佳視點、主最佳視點P_k,i,j (x_c ,y_c ,Z₀ ). . . Best viewpoint, main best viewpoint

P’_k,i,j(x’_c,y_c,Z₀)．．．移動後之最佳視點、次最佳視點P'_k,i,j (x'_c ,y_c ,Z₀ ). . . Best view point, sub-optimal view point after moving

P_0,-1,1、P_0,0,0、P_0,0,1、P_0,1,0．．．最佳視點之位置P_0,-1,1 , P_0,0,0 , P_0,0,1 , P_0,1,0 . . . Best viewpoint location

x_c．．．最佳視點之x座標x_c . . . X coordinate of the best viewpoint

y_c．．．最佳視點之y座標y_c . . . y coordinate of the best viewpoint

Δx_c．．．最佳視點可調變間距Δx_c . . . Optimal viewpoint adjustable pitch

Δx_c0．．．最佳視點可調變最小間距Δx_c0 . . . Optimal viewpoint adjustable minimum spacing

ΔX_OL．．．容許觀賞區重疊區域之寬度ΔX_OL . . . Allow the width of the overlapping area of the viewing area

i．．．水平可視區編號i. . . Horizontal viewable area number

j．．．視景數編號j. . . Number of views

k．．．垂直可視區編號k. . . Vertical viewable area number

L_H．．．水平最佳視點間距L_H . . . Horizontal best viewpoint spacing

L_V．．．垂直最佳視點間距L_V . . . Vertical best viewpoint spacing

．．．左影像 . . . Left image

．．．右影像 . . . Right image

_HP_k,i,j⁺(x_c+Δx_H,y_c,Z₀)．．．水平容許觀賞範圍右端點之位置_H P_k,i,j⁺ (x_c +Δx_H ,y_c ,Z₀ ). . . The horizontal allows the position of the right end of the viewing range

_HP_k,i,j^-(x_c-Δx_H,y_c,Z₀)．．．水平容許觀賞範圍左端點之位置_H P_k,i,j^- (x_c -Δx_H , y_c , Z₀ ). . . The horizontal allows the position of the left end of the viewing range

Δx_H．．．半水平容許觀賞範圍Δx_H . . . Semi-level allowable viewing range

_VP_k,i,j⁺(x_c,y_c+Δy_V,Z₀)．．．垂直容許觀賞範圍右端點之位置_V P_k,i,j⁺ (x_c ,y_c +Δy_V ,Z₀ ). . . Vertically allows the position of the right end of the viewing range

_VP_k,i,j^-(x_c,y_c-Δy_V,Z₀)．．．垂直容許觀賞範圍左端點之位置_V P_k,i,j^- (x_c ,y_c -Δy_V ,Z₀ ). . . Vertically allows the position of the left end of the viewing range

Δy_V．．．半垂直容許觀賞範圍Δy_V . . . Semi-vertical allowable viewing range

Y_i.j(x,y)、Y_i,j,Δ=0(x,y)．．．主中心線Y_ij (x, y), Y_{i, j, Δ = 0} (x, y). . . Main centerline

Y’_i,j(x,y)、Y_i,j,Δ≠0(x,y)．．．次中心線Y'_i,j (x,y), Y_i,j,Δ≠0 (x,y). . . Secondary centerline

f．．．左、右攝影機之焦距f. . . Left and right camera focal length

S．．．左、右攝影機光軸間距S. . . Left and right camera optical axis spacing

H．．．左、右攝影機裝置高度H. . . Left and right camera unit height

X_LY_LZ_L．．．左影像座標系X_L Y_L Z_L . . . Left image coordinate system

X_RY_RZ_R．．．右影像座標系X_R Y_R Z_R . . . Right image coordinate system

P(X_P,Y_P,Z_P)．．．物點座標P(X_P , Y_P , Z_P ). . . Point coordinates

I_L(x_L,y_L,0)．．．物點左成像位置I_L (x_L , y_L , 0). . . Object point left imaging position

I_R(x_R,y_R,0)．．．物點右成像位置I_R (x_R , y_R , 0). . . Object point right imaging position

E_L=(X_L,Y_L,Z_L)．．．XYZ座標係中左眼之座標E_L = (X_L , Y_L , Z_L ). . . The coordinates of the left eye in the XYZ coordinate system

E_R=(X_R,Y_R,Z_R)．．．XYZ座標係中右眼之座標E_R = (X_R , Y_R , Z_R ). . . The coordinates of the right eye in the XYZ coordinate system

i_L,L=(x_L,L,y_L,L,0)．．．X_LY_LZ_L座標係中左眼球中心之座標i_L,L =(x_L,L ,y_L,L ,0). . . The coordinates of the center of the left eye in the X_L Y_L Z_L coordinate system

i_L,R=(x_L,R,y_L,R,0)．．．X_LY_LZ_L座標係中右眼球中心之座標i_L,R =(x_L,R ,y_L,R ,0). . . The coordinates of the center of the right eye in the X_L Y_L Z_L coordinate system

i_R,L=(x_R,L,y_R,L,0)．．．X_RY_RZ_R座標係中左眼球中心之座標i_R,L =(x_R,L ,y_R,L ,0). . . The coordinates of the center of the left eye in the X_R Y_R Z_R coordinate system

i_R,R=(x_R,R,y_R,R,0)．．．X_RY_RZ_R座標係中右眼球中心之座標i_R,R =(x_R,R ,y_R,R ,0). . . The coordinates of the center of the right eye in the X_R Y_R Z_R coordinate system

ΔZ₀．．．可容許最佳觀賞距離之偏差量ΔZ₀ . . . Allowable deviation of the best viewing distance

Δφ．．．可容許水平觀賞角度之偏差量Δφ. . . Allowable deviation of horizontal viewing angle

Δρ．．．可容許傾斜觀賞角度之偏差量Δρ. . . Allowable deviation of tilt viewing angle

Y_E．．．最佳觀賞條件下，左右眼之Y軸座標Y_E . . . Under the best viewing conditions, the Y-axis coordinates of the left and right eyes

x(i,j,Δ=0)．．．主最佳視點x(i,j,Δ=0). . . Main best viewpoint

x(i,j,Δ≠0)．．．次最佳視點x(i,j,Δ≠0). . . Suboptimal viewpoint

L_L、L_R．．．通過左右眼位置之斜線L_L , L_R . . . Slash through the left and right eye positions

x_L0、x_R0．．．L_L、L_R與X軸交會點之座標x_L0 , x_R0 . . . The coordinates of L_L , L_R and X-axis intersection

x_max、y_max．．．最佳可視面之範圍x_max , y_max . . . Scope of the best visible surface

Ω_H．．．水平可視角Ω_H . . . Horizontal viewing angle

Ω_V．．．垂直可視角Ω_V . . . Vertical viewing angle

i_max．．．最佳可視面所對應之最大水平可視區編號i_max . . . Maximum horizontal viewable area number corresponding to the best visible surface

k_max．．．最佳可視面所對應之最大垂直可視區編號k_max . . . The maximum vertical viewable area number corresponding to the best visible surface

圖1所示，係一般R、G、B次畫素為水平條狀排列平面顯示器螢幕之示意圖。As shown in FIG. 1, the general R, G, and B pixels are schematic diagrams of a horizontal strip-shaped flat display screen.

圖2～9所示，係各種具右傾斜特徵之多視景3D合成影像。Figures 2-9 show various multi-view 3D composite images with right-tilt features.

圖10所示，係不具傾特徵之多視景3D合成影像Figure 10 shows a multi-view 3D composite image without tilting features.

圖11所示，係具左傾斜特徵之多視景3D合成影像。As shown in Fig. 11, a multi-view 3D composite image with a left-tilt feature is attached.

圖12所示，係雙視景用傾斜條狀視差光柵結構之示意圖。FIG. 12 is a schematic view showing a structure of a tilt strip-shaped parallax barrier for a dual view.

圖13所示，係最佳觀賞面上最佳視點分佈之示意圖。Figure 13 is a schematic diagram showing the best viewpoint distribution on the best viewing surface.

圖14所示，係雙視景3D合成影像顯示原理之示意圖。FIG. 14 is a schematic diagram showing the principle of dual view 3D synthetic image display.

圖15所示，係n=2、m=3、且k=0時，最佳視點P_k,i,j(x_c,y_c,Z₀)中i、j定義之示意圖。Figure 15 is a diagram showing the definitions of i and j in the optimal viewpoint P_k,i,j (x_c ,y_c ,Z₀ ) when n=2, m=3, and k=0.

圖16所示，係n=2、m=3、且k=0時，各水平最佳視點之座標。As shown in Fig. 16, when n = 2, m = 3, and k = 0, the coordinates of each horizontal optimum viewpoint are shown.

圖17所示，係n=4、m=3、且k=0時，最佳視點P_k,i,j(x_c,y_c,Z₀)中i、j定義之示意圖。Figure 17 is a diagram showing the definitions of i and j in the optimal viewpoint P_k,i,j (x_c ,y_c ,Z₀ ) when n=4, m=3, and k=0.

圖18所示，係n=4、m=3、且k=0時，各水平最佳視點之座標。As shown in Fig. 18, when n=4, m=3, and k=0, the coordinates of the best viewpoints of each level are shown.

圖19所示，係ΔB_H=B_H/2時，ΔB_H與ΔX_VF關係之示意圖。Fig. 19 is a schematic diagram showing the relationship between ΔB_H and ΔX_VF when ΔB_H = B_H /2.

圖20所示，係ΔB_H=2B_H/3時，ΔB_H與ΔX_VF關係之示意圖。Figure 20 is a graph showing the relationship between ΔB_H and ΔX_VF when ΔB_H = 2B_H /3.

圖21～26所示，係由各種多視景3D合成影像之示意圖。21 to 26 are schematic views of images synthesized by various multi-view 3D images.

圖27所示，係雙視景用傾斜條狀視差光柵垂直方向光學作用之示意圖。Fig. 27 is a schematic view showing the optical action in the vertical direction of the oblique strip-shaped parallax barrier for the dual view.

圖28所示，係ΔB_V=B_V/2時，ΔB_V與ΔY_VF關係之示意圖。Fig. 28 is a diagram showing the relationship between ΔB_V and ΔY_VF when ΔB_V = B_V /2.

圖29所示，係ΔB_V=2B_V/3時，ΔB_V與ΔY_VF關係之示意圖。Fig. 29 is a view showing the relationship between ΔB_V and ΔY_VF when ΔB_V = 2B_V /3.

圖30所示，係具水平與垂直容許觀賞範圍特徵之最佳視點之示意圖Figure 30 is a schematic diagram showing the best viewpoint of the horizontal and vertical allowable viewing range features.

圖31所示，係具傾斜角θ分佈特徵之容許觀賞範圍與鬼影區之示意圖。Figure 31 is a schematic view showing the allowable viewing range and the ghosting area of the skew angle θ distribution feature.

圖32～37所示，係各種具不同Δ值之雙視景3D合成影像之示意圖。32 to 37 are schematic views of various dual-view 3D composite images having different delta values.

圖38～43所示，係Δ與P_k,i,j(x_c,y_c,Z₀)關係之示意圖。38 to 43 are diagrams showing the relationship between Δ and P_k,i,j (x_c , y_c , Z₀ ).

圖44所示，係Δ=0時，中心線、邊界線位置之示意圖。Fig. 44 is a view showing the positions of the center line and the boundary line when Δ = 0.

圖45所示，係Δ=1時，中心線、邊界線位置改變之示意圖。Fig. 45 is a view showing a change in the position of the center line and the boundary line when Δ = 1.

圖46所示，係Δ=0與Δ=1之中心線、邊界線位置做重疊處理之示意圖。Fig. 46 is a schematic diagram showing the overlapping processing of the center line and the boundary line position of Δ = 0 and Δ = 1.

圖47～48所示，係立體攝影構成與裝置位置座標之示意圖。47 to 48 are schematic views showing the stereoscopic photographing configuration and the position coordinates of the apparatus.

圖49所示，係立體攝影裝置之示意圖。Fig. 49 is a schematic view showing a stereoscopic photographing apparatus.

圖50～52所示，係最佳觀賞條件設定之示意圖。Figures 50 to 52 show schematic diagrams of optimal viewing conditions.

圖53所示，係Δ=0、1、2時Y_i,j,Δ(x,y)之示意圖。Fig. 53 is a schematic diagram showing Y_{i, j, Δ} (x, y) when Δ = 0, 1, 2.

圖54所示，係Δ=0、-1、-2時Y_i,j,Δ(x,y)之示意圖。Fig. 54 is a view showing Y_{i, j, Δ} (x, y) when Δ = 0, -1, -2.

圖55所示，係Δ=0、1、2與Δ=-0、-1、-2時，計算取得Y_i,j,Δ(x,y)與X軸交點座標值x(i,j,Δ)之圖表。As shown in Fig. 55, when Δ = 0, 1, 2, and Δ = -0, -1, -2, the calculation obtains Y_{i, j, Δ} (x, y) and the X-axis intersection point value x (i, j) , Δ) chart.

圖56所示，係於|Δ|≦m之條件下，主最佳視點x(i=0,j=0,Δ=0)位置變化之圖表。Fig. 56 is a graph showing the positional change of the main optimum viewpoint x (i = 0, j = 0, Δ = 0) under the condition of |Δ|≦m.

圖57所示，係通過該左右眼位置(x_L,y_L,z_L)、(x_R,y_R,z_R)之斜線L_L、L_R之示意圖。57 is a schematic diagram showing oblique lines L_L and L_R passing through the left and right eye positions (x_L , y_L , z_L ), (x_R , y_R , z_R ).

圖58所示，係最佳可視面構成之示意圖。Figure 58 is a schematic view showing the configuration of the best visible surface.

圖59所示，係最佳可視面所對應最大水平可視區編號之示意圖。Figure 59 is a schematic diagram of the maximum horizontal viewable area number corresponding to the best visible surface.

圖60所示，係最佳可視面所對應最大垂直可視區編號之示意圖。Figure 60 is a schematic diagram showing the maximum vertical viewing area number corresponding to the best visible surface.

圖61所示，係對於雙視景顯示(n=2、m=3)、且於i=0、j=0之可視區為條件，x(i,j,Δ)構成之示意圖。Fig. 61 is a schematic diagram showing the configuration of x(i, j, Δ) for the dual view display (n = 2, m = 3) and the visible area of i = 0, j = 0.

圖62所示，係對於四視景顯示(n=4、m=3)、且於i=0、j=0、與i=1、j=0之可視區為條件，x(i,j,Δ)構成之示意圖。As shown in Fig. 62, for the four-view display (n=4, m=3), and the visible area of i=0, j=0, and i=1, j=0, x(i,j , Δ) is a schematic diagram.

圖63所示，係對於四視景顯示(n=4、m=3)、且於i=0、j=2之可視區為條件，x(i,j,Δ)構成之示意圖。63 is a schematic diagram showing the configuration of x(i, j, Δ) for the four-view display (n=4, m=3) and the visible area of i=0 and j=2.

圖64所示，係本發明實施例之示意圖。Figure 64 is a schematic view of an embodiment of the present invention.

400．．．本發明之實施例400. . . Embodiment of the present invention

410．．．觀賞位置即時檢測方法410. . . Instant detection method for viewing position

412．．．一對左、右攝影裝置412. . . a pair of left and right photographic devices

414．．．左右影像對應之程序414. . . Program corresponding to left and right images

416．．．三次元座標轉換計算之程序416. . . Three-dimensional coordinate conversion calculation program

418．．．觀賞條件最佳化之程序418. . . Program for optimizing viewing conditions

420．．．觀賞位置與視景最佳對位之方法420. . . Method for viewing the best alignment between position and view

422．．．左右眼之特徵座標計算之程序422. . . Procedure for calculating the coordinates of the left and right eyes

424．．．最佳觀賞線上最佳視點座標計算之程序424. . . Best viewing line coordinates calculation program

426．．．視點與視景對位之程序426. . . Program for viewing point and view

430．．．動態多視景3D影像合成之方法430. . . Dynamic multi-view 3D image synthesis method

432．．．多視景影像432. . . Multi-view image

434．．．多視景3D影像合成之程序434. . . Multi-view 3D image synthesis program

440．．．平面顯示器螢幕440. . . Flat panel display

450．．．靜態視差光柵裝置450. . . Static parallax barrier device

452．．．靜態視差光柵裝置設計之方法452. . . Method for designing static parallax barrier device

454．．．觀賞自由度最佳化之方法454. . . Method of optimizing viewing freedom

10．．．左眼10. . . Left eye

11．．．右眼11. . . Right eye

XYZ．．．螢幕座標系XYZ. . . Screen coordinate system

Z₀．．．最佳觀賞距離Z₀ . . . Best viewing distance

E_L．．．XYZ座標係中左眼之座標E_L . . . The coordinates of the left eye in the XYZ coordinate system

E_R．．．XYZ座標係中右眼之座標E_R . . . The coordinates of the right eye in the XYZ coordinate system

Δ．．．橫向位移相位Δ. . . Lateral displacement phase

Σ_n．．．多視景3D合成影像Σ_n . . . Multi-view 3D composite image

Claims (29)

Translated fromChinese

一種三次元影像顯示之方法，針對裸眼視三次元影像顯示之缺失，透過以下方法與元件之實施，可於最佳可視面上，有效解決鬼影、假立體影像、與水平與垂直方向觀賞自由度不足之問題，達到大幅提高3D影像品質與使用方便性之目的，其係包括有：一觀賞位置即時檢測之方法，係利用一對左、右攝影裝置，透過攝影、影像處理，於左、右影像座標系下，從左、右攝影裝置所取出之2D影像中，以檢測出左、右眼球之(或者是瞳孔)中心位置(i_L,L、i_L,R)、與右眼球之(或者是瞳孔)中心位置(i_R,L、i_R,R)，再利用一左右影像對應之程序、一三次元座標轉換計算之程序、與一觀賞條件最佳化之程序，於螢幕座標系下，可取得及輸出一左眼三次元之位置E_L=(X_L,Y_E,Z₀)、與右眼三次元之位置E_R=(X_R,Y_E,Z₀)；一觀賞位置與視景最佳對位之方法，係根據該左、右眼三次元位置E_L、E_R，透過一左右眼之特徵座標計算之程序、一最佳觀賞線上最佳視點座標計算之程序、與一視點與視景對位之程序，以計算取得及輸出一橫向位移相位Δ；一動態多視景3D影像合成之方法，係對於一多視景影像，根據該橫向位移相位Δ與一多視景3D影像合成之程序，以產生一多視景3D合成影像Σ_n；一平面顯示器螢幕，係接收與顯示該多視景3D合成影像Σ_n；以及一靜態視差光柵裝置，係為一靜態視景分離裝置，對於該多視景3D合成影像Σ_n，可於最佳觀賞距離上，提供一最佳觀賞面，並於該最佳觀賞面上，提供多數個最佳視點，可於該最佳視點處，作視景分離之光學作用，達到個別呈現單一視景影像之目的；上述視差光柵之光學結構，係透過一靜態視差光柵裝置設計之方法與一觀賞自由度最佳化之方法，以達到最佳化設計之目的。A three-dimensional image display method for the lack of naked-eye view three-dimensional image display, through the following methods and components, can effectively solve ghost images, false stereo images, and horizontal and vertical viewing freedom on the best visible surface The problem of insufficient degree is to achieve the purpose of greatly improving the quality and ease of use of 3D images. The system includes: a method for instantaneous detection of a viewing position, using a pair of left and right photographic devices, through photography, image processing, on the left, Under the right image coordinate system, the 2D images taken from the left and right photographic devices are used to detect the center position (i_{L, L} , i_{L, R} ) of the left and right eyeballs (i_{, L} , i_{L, R} ) and the right eyeball. (or the pupil) center position (i_{R, L} , i_{R, R} ), and then use a program corresponding to the left and right images, a program for calculating the calculation of a three-dimensional coordinate, and a program for optimizing the viewing conditions on the screen. Under the coordinate system, the position of the left eye three-dimensional element E_L = (X_L , Y_E , Z₀ ) and the position of the right eye three-dimensional element E_R = (X_R , Y_E , Z₀ ) can be obtained and output; The method of viewing the best alignment between the position and the view is based on the left and right Three-dimensional position E_L, E_R, wherein the program is calculated through the left and right of a coordinate, the program calculates a best view point coordinate optimal viewing line, with a view to the application and a view of the bit, in order to calculate and obtain the output a Lateral displacement phase Δ; a dynamic multi-view 3D image synthesis method for generating a multi-view 3D composite image according to the horizontal displacement phase Δ and a multi-view 3D image synthesis process for a multi-view image Σ_n ; a flat-panel display screen for receiving and displaying the multi-view 3D composite image Σ_n ; and a static parallax barrier device, which is a static view separating device for the multi-view 3D synthetic image Σ_n Providing an optimal viewing surface at the optimal viewing distance, and providing the best viewing point on the optimal viewing surface, the optical effect of the visual separation can be achieved at the optimal viewing point to achieve a single single presentation For the purpose of the visual image; the optical structure of the parallax barrier described above is optimized by a method of designing a static parallax barrier device and a method for optimizing the degree of freedom of viewing.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該平面顯示器螢幕，係可由一般之液晶螢幕、電漿螢幕、或是OLED螢幕所構成；該螢幕係由N×M個RGB次畫素、或是N×M個RGBW次畫素所構成，其中，N為構成該顯示器螢幕水平方向(X軸)次畫素之總數、M則為構成該顯示器螢幕垂直方向(Y軸)次畫素之總數、R為紅色、G為綠色、B為藍色、W為白色；該單一個次畫素具有P_H×P_V之大小，其中，P_H為次畫素之水平寬度、P_V為次畫素之垂直高度。另外，設置一螢幕座標系XYZ，令該螢幕座標系之原點，係設置於該螢幕之中心；該螢幕座標系之X軸，係設置於水平之方向；該螢幕座標系之Y軸，係設置於垂直之方向；該螢幕座標系之Z軸，則以垂直於該顯示器螢幕之方向設置。The method for displaying a three-dimensional image according to claim 1, wherein the flat display screen is formed by a general liquid crystal screen, a plasma screen, or an OLED screen; the screen is composed of N×M RGB Sub-pixels, or N × M RGBW sub-pixels, where N is the total number of sub-pixels in the horizontal direction (X-axis) of the display screen, and M is the vertical direction (Y-axis) of the display screen. The total number of sub-pixels, R is red, G is green, B is blue, and W is white; the single sub-pixel has a size of P_H × P_V , where P_H is the horizontal width of the sub-pixel, P_V is the vertical height of the sub-pixel. In addition, a screen coordinate system XYZ is set, and the origin of the screen coordinate system is set at the center of the screen; the X-axis of the screen coordinate system is set in the horizontal direction; the Y-axis of the screen coordinate system is Set in the vertical direction; the Z coordinate of the screen coordinate system is set perpendicular to the display screen.如申請專利範圍第2項所述之三次元影像顯示之方法，其中該次畫素之排列，係可為RGB為水平條狀條狀排列、RGB為垂直條狀條狀排列、RGB為馬賽克排列、RGB為三角狀排列、或RGBW為Pentile之排列。For example, the method for displaying a three-dimensional image according to item 2 of the patent application scope, wherein the arrangement of the pixels is RGB is a horizontal strip strip arrangement, RGB is a vertical strip strip arrangement, and RGB is a mosaic arrangement. RGB is arranged in a triangle, or RGBW is an arrangement of Pentile.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該多視景影像，係由n個單一視景影像V_k所構成，並可根據以下公式表示：其中，各參數如下定義：～V_k影像中位於(i,j)位置之次畫素影像資料；N～顯示器螢幕水平方向次畫素之總數；M～顯示器螢幕垂直方向次畫素之總數；j、i～單一個次畫素水平與垂直位置之編號，且0≦j≦N-1、0≦i≦M-1；n～總視景數，且n≧2；k～視景編號數，且0≦k<n。The method as defined in claim 1 of the scope of the item of three-dimensional image display, wherein the multi-view images is constituted by the n-based single view image V_k, can be expressed by the following formula: Among them, the parameters are defined as follows: The number of sub-pixels in the (i, j) position in the ~V_k image; the total number of sub-pixels in the horizontal direction of the N to the display screen; the total number of sub-pixels in the vertical direction of the M to the display screen; j, i to single times The number of the horizontal and vertical positions of the pixel, and 0≦j≦N-1, 0≦i≦M-1; n~the total number of views, and n≧2;k~the number of the view number, and 0≦k< n.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該多視景3D影像合成之程序，係對於該多視景影像，透過以下公式，以產生該多視景3D合成影像Σ_n：其中，其中，各參數與函數int、Mod如下定義：～V_Λ影像中位於(i,j)位置之次畫素影像資料Λ～視景編號數，且Λ<n;n～總視景數；m～橫向最小顯示單元次畫素構成之數目；Q～縱向最小顯示單元次畫素構成之數目；Δ～橫向位移相位；Π～橫向位移振幅；j、i～單一個次畫素水平與垂直位置之編號，且0≦j≦N-1、0≦i≦M-1；int～為取整數之函數；Mod～為取餘數之函數。The method for displaying a three-dimensional image according to claim 1, wherein the multi-view 3D image synthesizing program generates the multi-view 3D synthetic image by using the following formula for the multi-view image._n : among them, Among them, each parameter and function int, mod are defined as follows: The number of sub-pixel image data Λ to view number at the (i, j) position in the ~V_Λ image, and Λ <n; n - total number of views; m - the number of sub-pixels in the horizontal minimum display unit; Q ~ the number of sub-pixels in the vertical minimum display unit; Δ ~ lateral displacement phase; Π ~ lateral displacement amplitude; j, i ~ single sub-pixel level and vertical position number, and 0 ≦ j ≦ N-1, 0≦i≦M-1; int~ is a function of integer; Mod~ is a function of remainder.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該多視景3D影像合成之程序，係對於該多視景影像，透過以下公式，以產生該多視景3D合成影像Σ_n：其中，其中，各參數與函數int、Mod如下定義：～V_Λ影像中位於(i,j)位置之次畫素影像資料Λ～視景編號數，且Λ<n;n～總視景數；m～橫向最小顯示單元次畫素構成之數目；Q～縱向最小顯示單元次畫素構成之數目；Δ～橫向位移相位；Π～橫向位移振幅；j、i～單一個次畫素水平與垂直位置之編號，且0≦j≦N-1、0≦i≦M-1；int～為取整數之函數；Mod～為取餘數之函數。The method for displaying a three-dimensional image according to claim 1, wherein the multi-view 3D image synthesizing program generates the multi-view 3D synthetic image by using the following formula for the multi-view image._n : among them, Among them, each parameter and function int, mod are defined as follows: The number of sub-pixel image data Λ to view number at the (i, j) position in the ~V_Λ image, and Λ <n; n - total number of views; m - the number of sub-pixels in the horizontal minimum display unit; Q ~ the number of sub-pixels in the vertical minimum display unit; Δ ~ lateral displacement phase; Π ~ lateral displacement amplitude; j, i ~ single sub-pixel level and vertical position number, and 0 ≦ j ≦ N-1, 0≦i≦M-1; int~ is a function of integer; Mod~ is a function of remainder.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該靜態視差光柵裝置設計之方法，係根據以下公式，以設計產生其水平方向之基本光學結構：其中，各參數之定義如下：B_H～透光元件之水平寬度；～遮蔽元件之水平寬度；L_H～水平最佳視點間距；θ～傾斜條狀視差光柵之傾斜角度；Z₀～最佳觀賞距離；L_B～傾斜條狀視差光柵之裝置距離；P_H～次畫素之水平寬度；n～總視景數；m～橫向最小顯示單元次畫素構成之數目；Q～縱向最小顯示單元次畫素構成之數目。The method for displaying a three-dimensional image according to claim 1, wherein the method for designing the static parallax barrier device is designed to generate a basic optical structure in a horizontal direction according to the following formula: Wherein, the definition of each parameter is as follows: B_H ~ horizontal width of the light-transmitting element; ~ horizontal width of the shielding element; L_H ~ horizontal optimal viewing point spacing; θ ~ inclined angle of oblique strip-shaped parallax barrier; Z₀ ~ optimal viewing distance; L_B ~ oblique strip-shaped parallax grating device distance; P_H ~ The horizontal width of the sub-pixels; n to the total number of views; m to the number of sub-pixels in the horizontal minimum display unit; Q to the number of sub-pixels in the vertical minimum display unit.如申請專利範圍第7項所述之三次元影像顯示之方法，其中該水平最佳視點間距L_H與雙眼平均間距L_E，係可具有以下之關係：L_H=L_E。The method of displaying a three-dimensional image as described in claim 7 wherein the horizontal optimum viewpoint distance L_H and the average distance L_{E of the} eyes have the following relationship: L_H = L_E .如申請專利範圍第7項所述之三次元影像顯示之方法，其中該透光元件開口水平寬度B_H之最佳化設計，係透過作一透光元件開口水平寬度縮減之處理，以取得一水平容許觀賞範圍ΔX_VF，該水平容許觀賞範圍ΔX_VF與該透光元件開口水平寬度縮減量ΔB_H，係具有以下之關係：ΔX_VF=R_x×L_H；其中，R_x=ΔB_H/B_H；其中，各參數之定義如下：R_x～水平觀賞自由度，且0≦R_x≦1；L_H～水平最佳視點間距。The method for displaying a three-dimensional image according to claim 7, wherein the optimized design of the horizontal width B_H of the light-transmitting element is processed by reducing the horizontal width of the opening of the light-transmitting element to obtain a The horizontal allowable viewing range ΔX_VF , which allows the viewing range ΔX_VF and the light-transmitting element opening horizontal width reduction amount ΔB_{H to} have the following relationship: ΔX_VF = R_x × L_H ; where R_x = ΔB_H / B_H ; wherein each parameter is defined as follows: R_x ~ horizontal viewing degree of freedom, and 0 ≦ R_x ≦ 1; L_H ~ horizontal optimal viewpoint spacing.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該靜態視差光柵裝置設計之方法，係根據以下公式，以設計產生其垂直方向之基本光學結構：其中，各參數之定義如下：B_V～透光元件垂直開口寬度；L_V～垂直最佳視點間距；Z₀～最佳觀賞距離；L_B～傾斜條狀視差光柵之裝置距離；m～橫向最小顯示單元次畫素構成之數目；Q～縱向最小顯示單元次畫素構成之數目；P_V～次畫素之垂直高度。The method for displaying a three-dimensional image according to claim 1, wherein the method for designing the static parallax barrier device is designed to generate a basic optical structure in a vertical direction according to the following formula: Among them, the definition of each parameter is as follows: B_V ~ vertical opening width of light-transmitting element; L_V ~ vertical optimal viewpoint spacing; Z₀ ~ optimal viewing distance; L_B ~ oblique strip-shaped parallax grating device distance; m ~ horizontal The minimum display unit is composed of the number of sub-pixels; the number of sub-pixels in the Q to the vertical minimum display unit; and the vertical height of the P_V to sub-pixels.如申請專利範圍第10項所述之三次元影像顯示之方法，其中該透光元件垂直開口寬度B_V與透光元件之水平寬度B_H，具有以下之關係：其中，各參數之定義如下：Q～縱向最小顯示單元次畫素構成之數目P_V～次畫素之垂直高度；P_H～次畫素之水平寬度。The method of displaying a three-dimensional image according to claim 10, wherein the vertical opening width B_V of the light transmitting element and the horizontal width B_{H of the} light transmitting element have the following relationship: Among them, each parameter is defined as follows: Q to the vertical minimum display unit sub-pixel composition number P_V ~ sub-pixel vertical height; P_H ~ sub-pixel horizontal width.如申請專利範圍第10項所述之一種三次元影像顯示之方法，其中該垂直最佳視點間距L_V與水平最佳視點間距L_H，具有以下之關係：其中，各參數之定義如下：Q～縱向最小顯示單元次畫素構成之數目；P_V～次畫素之垂直高度；P_H～次畫素之水平寬度；θ～傾斜條狀視差光柵之傾斜角度。A method for displaying a three-dimensional image according to claim 10, wherein the vertical optimum viewpoint spacing L_V and the horizontal optimal viewpoint spacing L_H have the following relationship: Among them, the definition of each parameter is as follows: Q ~ the number of sub-pixels in the vertical minimum display unit; the vertical height of P_V ~ sub-pixels; the horizontal width of P_H ~ sub-pixels; the inclination of θ ~ oblique strip-shaped parallax grating angle.如申請專利範圍第10項所述之三次元影像顯示之方法，其中該透光元件開口垂直寬度B_V之最佳化設計，係透過作一透光元件開口垂直寬度縮減之處理，以取得一垂直容許觀賞範圍ΔY_VF，該垂直容許觀賞範圍ΔY_VF與該透光元件開口垂直寬度縮減量ΔB_V，係具有以下之關係：ΔY_VF=R_Y×L_V；其中，R_Y=ΔB_V/B_V；其中，各參數之定義如下：R_Y～垂直觀賞自由度，且0≦R_x≦1；L_V～垂直最佳視點間距。The method for displaying a three-dimensional image according to claim 10, wherein the optimized design of the vertical width B_V of the transparent member is processed by reducing the vertical width of the opening of the transparent member to obtain a The vertical allowable viewing range ΔY_VF , the vertical allowable viewing range ΔY_VF and the vertical width reduction amount ΔB_{V of} the light transmitting element opening have the following relationship: ΔY_VF = R_Y × L_V ; wherein R_Y = ΔB_V / B_V ; wherein each parameter is defined as follows: R_Y ~ vertical viewing degree of freedom, and 0 ≦ R_x ≦ 1; L_V ~ vertical optimum viewpoint spacing.如申請專利範圍第13項所述之三次元影像顯示之方法，其中該垂直觀賞自由度R_Y與水平觀賞自由度R_x，係可具有以下之關係：R_Y=R_X。The method of displaying a three-dimensional image according to claim 13 , wherein the vertical viewing degree of freedom R_Y and the horizontal viewing degree of freedom R_x have the following relationship: R_Y =R_X .如申請專利範圍第13項所述之三次元影像顯示之方法，其中該垂直容許觀賞範圍ΔY_VF與水平容許觀賞範圍ΔX_VF，係可具有以下之關係：The method for displaying a three-dimensional image according to claim 13 wherein the vertical allowable viewing range ΔY_VF and the horizontal allowable viewing range ΔX_VF have the following relationships:如申請專利範圍第1項所述之三次元影像顯示之方法，其中該觀賞自由度最佳化之方法，係令相鄰兩容許觀賞區間之重疊區域寬度ΔX_OL，具有下式之關係：ΔX_OL=(R_x-1/m)×L_H＞0；其中，各參數之定義如下：R_x～水平觀賞自由度；m～橫向最小顯示單元次畫素構成之數目；L_H～水平最佳視點間距。The method for displaying a three-dimensional image according to claim 1, wherein the method for optimizing the viewing degree of freedom is to make the overlapping region width ΔX_{OL of} two adjacent viewing intervals have the following relationship: ΔX_OL = (R_x -1/m) × L_H >0; wherein each parameter is defined as follows: R_x ~ horizontal viewing degree of freedom; m ~ horizontal minimum display unit sub-pixel composition number; L_H ~ level most Good view point spacing.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該靜態視差光柵之裝置，係可由具有垂直條狀式視差光柵、傾斜條狀式視差光柵、或傾斜格狀式視差光柵之結構所構成。The method for displaying a three-dimensional image according to claim 1, wherein the static parallax barrier device comprises a vertical stripe-type parallax barrier, a tilted strip-type parallax barrier, or a tilted lattice-type parallax barrier. Structured.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該多數個最佳視點之位置，於螢幕座標系中，係可以P_k,i,j(x_c,y_c,Z₀)表示，並具有下式之關係：x_c=[n×i-(n-1)/2+j-k]×L_H；y_c=k×L_V；另外，該多數個最佳視點P_k,i,j(x_c,y_c,Z₀)，係具水平容許觀賞範圍ΔX_VF與垂直容許觀賞範圍ΔY_VF，可根據光學結構傾斜之特徵，延該傾斜角θ做一分佈，以構成具有水平方向重複交錯排列特徵之容許觀賞區與鬼影區，該容許觀賞區，可藉由一中心線Y_i,j(x,y)、與兩邊界線Y_i,j⁺(x,y)、Y_i,j^-(x,y)以構成，並具有下式之關係：中心線Y_i,j(x,y)，如下式表示：y=f(θ){x-[n×i-(n-1)/2+j]×L_H}　(3)右邊界線Y_i,j⁺(x,y)，如下式表示：y=f(θ){x-[n×i-(n-1)/2+j+R_x/2]×L_H}　(4)左邊界線Y_i,j^-(x,y)，如下式表示：y=f(θ){x-[n×i-(n-1)/2+j-R_x/2]×L_H}　(5)其中，對於具右傾斜結構之視差光柵裝置，該f(θ)具有下式之關係：f(θ)=-tanθ；對於具左傾斜結構之視差光柵裝置，該f(θ)則由下式表示：f(θ)=tanθ；對於具垂直結構之視差光柵裝置，該θ=0、且f(θ)=0，該Y_i,j(x,y)、Y_i,j⁺(x,y)、Y_i,j^-(x,y)則成為垂直線，可個別由下式表示：x=[n×i-(n-1)/2+j]×L_H　(6)x=[n×i-(n-1)/2+j+R_x/2]×L_H　(7)x=[n×i-(n-1)/2+j-R_x/2]×L_H　(8)另外，對於式(3)～(5)所描述之該中心線Y_i,j(x,y)、邊界線Y_i,j⁺(x,y)、Y_i,j^-(x,y)，當令y=0時，所取得之x值，係如式(6)～(8)所示；亦即，對於具傾斜結構、與垂直結構之視差光柵裝置，在z=Z₀、y=0之水平線上，係具有相同之視景分離之光學作用；該z=Z₀、y=0之水平線，即為最佳觀賞線；另外，對於上述各公式中，其所使用之各參數如下定義：Z₀～最佳觀賞距離；n～總視景數；i～水平可視區編號；j～視景數編號；k～垂直可視區編號；L_H～水平最佳視點間距；L_V～垂直最佳視點間距；θ～傾斜條狀視差光柵之傾斜角度。The method for displaying a three-dimensional image according to claim 1, wherein the position of the plurality of optimal viewpoints is P_{k, i, j} (x_c , y_c , Z_{0 )} in the screen coordinate system. Said, and has the relationship of: x_c = [n × i - (n-1) / 2 + jk] × L_H ; y_c = k × L_V ; in addition, the majority of the best viewpoint P_{k , i, j} (x_c , y_c , Z₀ ), the horizontal allowable viewing range ΔX_VF and the vertical allowable viewing range ΔY_VF , which can be distributed according to the characteristics of the tilt of the optical structure to form a distribution An allowable viewing area and a ghosting area having repeating staggered features in a horizontal direction, the allowable viewing area being represented by a center line Y_i,j (x,y), and two boundary lines Y_i,j⁺ (x,y) , Y_i,j^- (x,y) are constructed and have the following relationship: the center line Y_i,j (x,y) is expressed as follows: y=f(θ){x-[n×i -(n-1)/2+j]×L_H } (3) Right boundary line Y_i,j⁺ (x,y), expressed as follows: y=f(θ){x-[n×i-( N-1)/2+j+R_x /2]×L_H } (4) Left boundary line Y_i,j^- (x,y), expressed as follows: y=f(θ){x-[n× I-(n-1)/2+jR_x /2]×L_H } (5) wherein, for a parallax barrier device having a right tilt structure, the f(θ) The relationship has the following formula: f(θ)=-tan θ; for a parallax barrier device having a left-inclined structure, the f(θ) is represented by the following formula: f(θ)=tan θ; for a parallax barrier device having a vertical structure , θ=0, and f(θ)=0, the Y_i,j (x,y), Y_i,j⁺ (x,y), Y_i,j^- (x,y) become vertical lines , can be expressed by the following formula: x = [n × i - (n-1) / 2 + j] × L_H (6) x = [n × i - (n-1) / 2 + j + R_x /2]×L_H (7)x=[n×i-(n-1)/2+jR_x /2]×L_H (8) In addition, for the description of the formulas (3) to (5) Center line Y_i,j (x,y), boundary line Y_i,j⁺ (x,y), Y_i,j^- (x,y), when y=0, the obtained x value is as Equations (6) to (8); that is, for a parallax barrier device having an inclined structure and a vertical structure, the optical effect of the same visual separation is obtained on the horizontal line of z=Z₀ and y=0. The horizontal line of z=Z₀ and y=0 is the best viewing line; in addition, for each of the above formulas, the parameters used are as follows: Z₀ ~ optimal viewing distance; n ~ total view number; i ~ horizontal viewing area number; j ~ the number of scene number; k ~ vertical viewing area number; L_H ~ horizontal optimum viewing distance; L_V Vertical optimum viewing distance; θ ~ inclination angle of inclination of the strip parallax barrier.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該一對左、右攝影裝置，係具有相同之光學成像系統，即具有相同焦距f之光學成像透鏡、與相同之影像感應器，於該左、右攝影裝置上，個別設置一左影像座標系X_LY_LZ_L、一右影像座標系X_RY_RZ_R；令該兩影像座標系之原點，係個別設置於該左、右攝影裝置影像感應器之中心，且該兩影像座標系與螢幕座標系之座標軸，具有平行之關係，於螢幕座標系下，令該兩影像座標系之原點座標，係個別為(-S/2,H,0)、(S/2,H,0)，其中，S為該左、右攝影裝置光軸間距，H則為裝置高度；另外，令Z_L、Z_R係個別設置於該左、右攝影裝置光軸上，亦即，該左、右攝影裝置之光軸，係平行於Z軸，該左、右眼球之(或者是瞳孔)中心座標，係可如下式表示：於左影像座標系中，該左眼球(或者是瞳孔)中心之座標：i_L,L=(x_L,L,y_L,L,0)；於左影像座標系中，該右眼球(或者是瞳孔)中心之座標：i_L,R=(x_L,R,y_L,R,0)；於右影像座標系中，左眼球(或者是瞳孔)中心之座標：i_R,L=(x_R,L,y_R,L,0)；於右影像座標系中，右眼球(或者是瞳孔)中心之座標：i_R,R=(x_R,R,y_R,R,0)；另外，因該左、右攝影裝置具有同樣光學特徵，可令y_L,L=y_R,L=y_L、且y_L,R=y_R,R=y_R。The method of displaying a three-dimensional image according to claim 1, wherein the pair of left and right photographic devices have the same optical imaging system, that is, an optical imaging lens having the same focal length f, and the same image sensing. On the left and right photographic devices, a left image coordinate system X_L Y_L Z_L and a right image coordinate system X_R Y_R Z_R are separately set; the origins of the two image coordinate systems are individually set. In the center of the image sensor of the left and right photographic devices, and the two image coordinate systems and the coordinate axis of the screen coordinate system have a parallel relationship, under the screen coordinate system, the origin coordinates of the two image coordinate systems are individually (-S/2, H, 0), (S/2, H, 0), where S is the optical axis spacing of the left and right photographic devices, and H is the height of the device; in addition, let Z_L , Z_R They are individually disposed on the optical axes of the left and right photographic devices, that is, the optical axes of the left and right photographic devices are parallel to the Z axis, and the center coordinates of the left and right eyeballs (or boring) are as follows Expression: in the left image coordinate system, the coordinates of the center of the left eye (or pupil): i_{L, L} =(x_L,L ,y_L,L ,0); in the left image coordinate system, the coordinates of the center of the right eye (or pupil): i_{L, R} = (x_{L, R} , y_{L, R} , 0); In the right image coordinate system, the coordinates of the center of the left eyeball (or pupil): i_{R, L} = (x_{R, L} , y_{R, L} , 0); in the right image coordinate system, the right eyeball ( Or the coordinates of the center of the pupil: i_{R, R} = (x_{R, R} , y_{R, R} , 0); in addition, because the left and right photographic devices have the same optical characteristics, y_{L, L} = y_{R , L} = y_L , and y_{L, R} = y_{R, R} = y_R .如申請專利範圍第1項所述之三次元影像顯示之方法，其中該左右影像對應之程序，係指將左、右影像座標系中之左、右眼球中心座標、與螢幕座標系中之左、右眼三次元座標，作一對應之處理，亦即，左眼位置E_L係由i_L,L與i_R,L所對應；而右眼位置E_R則由i_L,R與i_R,R所對應。For example, the method for displaying the three-dimensional image according to Item 1 of the patent application, wherein the program corresponding to the left and right images refers to the left and right eye center coordinates in the left and right image coordinate systems, and the left in the screen coordinate system. , the right-eye three-dimensional coordinates for a corresponding one of the process, i.e., the position of the left eye E_L of line i_{L, L} and i_R, corresponding_L; and the right eye E_R by position i_{L, R} and i_{R ,} corresponding to_R.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該三次元座標轉換計算之程序，係透過一影像座標系與螢幕座標系間之座標轉換，將成像於影像座標系上之左眼座標i_L,L與i_R,L，轉換成螢幕座標系上之三次元座標E_L=(X_L,Y_L,Z_L)，以及，將右眼座標i_L,R、i_R,R，轉換成影像座標系上之三次元座標E_R=(X_R,Y_R,Z_R)。The method of displaying a three-dimensional image according to claim 1, wherein the three-dimensional coordinate conversion calculation process is performed by image coordinate conversion between an image coordinate system and a screen coordinate system, and is imaged on the image coordinate system. The left eye coordinates i_{L, L} and i_{R, L are} converted into the three-dimensional coordinates E_L = (X_L , Y_L , Z_L ) on the screen coordinate system, and the right eye coordinates i_{L, R} , i_{R , R} , converted to the three-dimensional coordinate E_R = (X_R , Y_R , Z_R ) on the image coordinate system.如申請專利範圍第21項所述之三次元影像顯示之方法，其中該影像座標系與螢幕座標系間之座標轉換，係具有以下之關係：左眼三次元之座標：右眼三次元之座標：For example, the method for displaying a three-dimensional image according to claim 21, wherein the coordinate conversion between the image coordinate system and the screen coordinate system has the following relationship: the coordinate of the left eye three-dimensional: The coordinates of the three-dimensional right eye:如申請專利範圍第1項所述之三次元影像顯示之方法，其中該觀賞條件最佳化之程序，主要係由以下最佳之觀賞條件所構成：一觀賞距離最佳化之條件，係由下式條件所構成：|Z_L-Z₀|＜ΔZ₀；|Z_R-Z₀|＜ΔZ₀；其中，ΔZ₀為可容許最佳觀賞距離之偏差量，亦即，Z_L、Z_R與Z₀之差距，需小於ΔZ₀；以及一正視螢幕最佳化之條件，係由下式條件所構成：其中，Δφ為可容許水平觀賞角度之偏差量、Δρ為可容許傾斜觀賞角度之偏差量、為x軸之單位向量，亦即，左右眼需正視螢幕，且水平觀賞角度之偏差量，需小於Δφ、且傾斜觀賞角度之偏差量，需小於Δρ；是以，上述之條件，更可簡化且如下表示：Y_L=Y_R=Y_E；Z_L=Z_R=Z₀；亦即，該觀賞條件之最佳化，係規範該觀賞者之觀賞位置，當該觀賞位置可滿足：(a)讓雙眼維持在同樣的最佳觀賞距離、(b)讓雙眼保持同樣之高度(即保持水平狀態)、(c)需讓雙眼正視螢幕等條件時，即可觀賞到具最佳品質之3D影像。The method for displaying a three-dimensional image as described in claim 1, wherein the program for optimizing the viewing condition is mainly composed of the following optimal viewing conditions: a condition for optimizing the viewing distance is The following condition is composed of: |Z_{L -} Z₀ | < ΔZ₀ ; | Z_{R -} Z₀ | < ΔZ₀ ; where ΔZ₀ is the deviation amount that can tolerate the best viewing distance, that is, Z_L , Z The difference between_R and Z₀ needs to be less than ΔZ₀ ; and the condition for optimizing the screen is composed of the following conditions: Where Δφ is the amount of deviation of the allowable horizontal viewing angle, and Δρ is the amount of deviation of the allowable tilt viewing angle, It is the unit vector of the x-axis, that is, the left and right eyes need to face the screen, and the deviation of the horizontal viewing angle needs to be smaller than Δφ, and the deviation of the oblique viewing angle needs to be smaller than Δρ. Therefore, the above conditions can be simplified. And is expressed as follows: Y_L = Y_R = Y_E ; Z_L = Z_R = Z₀ ; that is, the optimization of the viewing condition is to standardize the viewing position of the viewer, when the viewing position can satisfy: ( a) Keep your eyes at the same optimal viewing distance, (b) Keep your eyes at the same height (ie, keep them level), (c) Have your eyes look at the screen, etc. Good quality 3D imagery.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該左、右攝影裝置，係可以內藏之方式、或者是以外掛之方式，裝置於行動電話、數位相機、攝影機、遊戲機、平板點腦、筆記型電腦、監視器、電視、3D電視等裝置之機殼之上。The method for displaying a three-dimensional image according to claim 1, wherein the left and right photographing devices are installed in a mobile phone, a digital camera, a camera, or a game in a built-in manner or in an external manner. On the case of a device, a tablet, a laptop, a monitor, a TV, a 3D TV, etc.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該左右眼特徵座標計算之程序，其計算之方法係令具有同樣傾斜角度θ之斜線L_L、L_R，個別通過該左、右眼之位置(X_L,Y_L,Z_L)、(X_R,Y_R,Z_R)，並與X軸個別交會於x_L0、x_R0，該x_L0、x_R0具有以下之關係：對於具右傾斜結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：x_L0=X_L+tan(θ)×Y_L；x_R0=X_R+tan(θ)×Y_R；對於具左傾斜結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：x_L0=X_L-tan(θ)×Y_L；x_R0=X_R-tan(θ)×Y_R；對於垂直結構之視差光柵裝置，該x_L0、x_R0係如下計算取得：x_L0=X_L；x_R0=X_R。The method for displaying a three-dimensional image according to claim 1, wherein the method for calculating the left and right eye feature coordinates is calculated by slanting lines L_L and L_R having the same inclination angle θ, and individually passing the left The position of the right eye (X_L , Y_L , Z_L ), (X_R , Y_R , Z_R ), and intersects with the X axis individually at x_L0 , x_R0 , and the x_L0 and x_R0 have the following relationship For a parallax barrier device with a right-inclined structure, the x_L0 and x_R0 are calculated as follows: x_L0 = X_L + tan(θ) × Y_L ; x_R0 = X_R + tan(θ) × Y_R ; For a parallax barrier device with a left-inclined structure, the x_L0 and x_R0 are calculated as follows: x_L0 =X_L -tan(θ)×Y_L ;x_R0 =X_R -tan(θ)×Y_R ; In a vertical structure parallax barrier device, the x_L0 and x_R0 are calculated as follows: x_L0 = X_L ; x_R0 = X_R .如申請專利範圍第1項所述之三次元影像顯示之方法，其中該最佳觀賞線上最佳視點座標計算之程序，係透過以下之公式，以計算該最佳視點之座標x(i,j,Δ)：x(i,j,Δ)=[n×i-(n-1)/2+j-Δ/m]×L_H；其中，各參數如下定義：n～總視景數；m～橫向最小顯示單元次畫素構成之數目；i～水平可視區編號；j～視景數編號；Δ～橫向位移相位；L_H～水平最佳視點間距。The method for displaying a three-dimensional image according to claim 1, wherein the program for calculating the optimal viewpoint coordinates on the optimal viewing line is calculated by the following formula to calculate the coordinates of the optimal viewpoint x (i, j). , Δ): x (i, j, Δ) = [n × i - (n-1) / 2 + j - Δ / m] × L_H ; wherein, each parameter is defined as follows: n ~ total number of views; m ~ horizontal minimum display unit sub-pixel composition number; i ~ horizontal viewable area number; j ~ view number number; Δ ~ lateral displacement phase; L_H ~ horizontal optimal view point spacing.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該視點與視景對位之程序，當以左眼位置為基準時，係由以下步驟所構成：步驟一、確認左右眼之位置(X_L,Y_E,Z₀)、(X_R,Y_E,Z₀)，是否存在於最佳可視面之範圍內。如果，滿足下式之關係，則跳至步驟二；若不滿足下式之關係，則宣告觀賞位置偏離最佳可視面範圍，跳至步驟五；|X_L|≦x_max；|X_R|≦x_max；|Y_E|≦y_max；步驟二、設定起始值，如下式：i=-i_max；j=0；步驟三、計算x(i,j,Δ)；步驟四、比對x_L0與x(i,j,Δ)，如下式：|x_L0-x(i,j,Δ)|≦L_H/2m　(9)情況1：若找到一組(i,j,Δ)參數，符合式(9)之關係，則將Δ代入式(1)、或(2)、並宣告3D眼睛追蹤成功，跳至步驟五；情況2：若找不到一組(i,j,Δ)參數，符合式(9)之關係，則令j=j+2；若j<n(即j未超出i可視區)，則跳至步驟三；若j≧n(即j已超出i可視區)，則令i=i+1；j=0；若i≦i_max，跳至步驟三；若i>i_max，宣告觀賞位置偏離最佳可視面圍，跳至步驟五；步驟五、結束比對其中，各參數之定義如下：x_max、y_max～該最佳可視面之範圍；i_max～最佳可視面所對應之最大水平可視區編號；i～水平可視區編號；j～視景數編號；n～總視景數；m～橫向最小顯示單元次畫素構成之數目；Δ～橫向位移相位；L_H～水平最佳視點間距。The method for displaying a three-dimensional image according to the first aspect of the patent application, wherein the program for aligning the viewpoint with the view, when based on the position of the left eye, is composed of the following steps: Step 1: confirming the left and right eyes The position (X_L , Y_E , Z₀ ), (X_R , Y_E , Z₀ ) is present in the range of the best visible surface. If the relationship of the following formula is satisfied, skip to step 2; if the relationship of the following formula is not satisfied, declare the viewing position to deviate from the optimal visible surface range, and skip to step 5; |X_L |≦x_max ;|X_R | ≦x_max ;|Y_E |≦y_max ;Step 2, set the starting value, as follows: i=-i_max ; j=0; Step 3, calculate x(i, j, Δ); Step 4, ratio For x_L0 and x(i,j,Δ), the following formula: |x_L0 -x(i,j,Δ)|≦L_H /2m (9) Case 1: If a set (i, j, Δ is found) ) parameter, in accordance with the relationship of equation (9), substituting Δ into equation (1), or (2), and declaring 3D eye tracking success, skip to step five; situation 2: if a group is not found (i, j , Δ) parameter, in accordance with the relationship of equation (9), let j = j + 2; if j < n (ie j does not exceed the i visible area), then jump to step three; if j ≧ n (ie j has exceeded i visible area), let i=i+1; j=0; if i≦i_max , skip to step 3; if i>i_max , declare the viewing position to deviate from the best visible surface, skip to step 5; five, wherein the end of the match, each parameter is defined as follows: x_max, y_max ~ range of the visible face of the optimum; i_max ~ best visible face of the visible region of the maximum level corresponding to the coding ; I ~ horizontal viewing area number; j ~ the number of scene number; n ~ the total number of visual scene; m ~ a minimum number of lateral sub-pixels constituting the display unit; Δ ~ lateral displacement phase; L_H ~ horizontal optimum viewing distance.如申請專利範圍第1項所述之三次元影像顯示之方法，其中該視點與視景對位之程序，當以右眼位置為基準時，係由以下步驟所構成：步驟一、確認左右眼之位置(X_L,Y_E,Z₀)、(X_R,Y_E,Z₀)，是否存在於最佳可視面之範圍內。如果，滿足下式之關係，則跳至步驟二；若不滿足下式之關係，則宣告觀賞位置偏離最佳可視面範圍，跳至步驟五；|X_L|≦x_max；|X_R|≦x_max；|Y_E|≦y_max；步驟二、設定起始值，如下式：i=-i_max；j=1；步驟三、計算x(i,j,Δ)；步驟四、比對x_R0與x(i,j,Δ)，如下式：|x_R0-x(i,j,Δ)|≦L_H/2m　(10)情況1：若找到一組(i,j,Δ)參數，符合式(10)之關係，則將Δ代入式(1)、或(2)、並宣告3D眼睛追蹤成功，跳至步驟五；情況2：若找不到一組(i,j,Δ)參數，符合式(4)之關係，則令j=j+2；若j<n(即j未超出i可視區)，則跳至步驟三；若j≧n(即j已超出i可視區)，則令i=i+1；j=1；若i≦i_max，跳至步驟三；若i>i_max，宣告觀賞位置偏離最佳可視面圍，跳至步驟五；步驟五、結束比對其中，各參數之定義如下：x_max、y_max～該最佳可視面之範圍；i_max～最佳可視面所對應之最大水平可視區編號；i～水平可視區編號；j～視景數編號；n～總視景數；m～橫向最小顯示單元次畫素構成之數目；Δ～橫向位移相位；L_H～水平最佳視點間距。The method for displaying a three-dimensional image according to the first aspect of the patent application, wherein the program for aligning the viewpoint with the view, when the position of the right eye is used as a reference, is composed of the following steps: Step 1: confirming the left and right eyes The position (X_L , Y_E , Z₀ ), (X_R , Y_E , Z₀ ) is present in the range of the best visible surface. If the relationship of the following formula is satisfied, skip to step 2; if the relationship of the following formula is not satisfied, declare the viewing position to deviate from the optimal visible surface range, and skip to step 5; |X_L |≦x_max ;|X_R | ≦x_max ;|Y_E |≦y_max ;Step 2, set the starting value, as follows: i=-i_max ; j=1; Step 3, calculate x(i, j, Δ); Step 4, ratio For x_R0 and x(i,j,Δ), the following formula: |x_R0 -x(i,j,Δ)|≦L_H /2m (10) Case 1: If a set (i, j, Δ is found) The parameter, in accordance with the relationship of equation (10), substituting Δ into equation (1), or (2), and declaring 3D eye tracking success, skip to step five; situation 2: if a group is not found (i, j , Δ) parameter, in accordance with the relationship of equation (4), let j = j + 2; if j < n (ie j does not exceed the i visible area), then jump to step three; if j ≧ n (ie j has exceeded i viewable area), let i=i+1;j=1; if i≦i_max , skip to step 3; if i>i_max , declare the viewing position to deviate from the best visible surface, skip to step 5; 5. End the comparison, the definition of each parameter is as follows: x_max , y_max ~ the range of the best visible surface; i_max ~ the best horizontal visible area corresponding to the best visible surface Number; i ~ horizontal visible area number; j ~ view number number; n ~ total view number; m ~ horizontal minimum display unit sub-pixel composition number; Δ ~ lateral displacement phase; L_H ~ horizontal optimal view point spacing .如申請專利範圍第1項所述之三次元影像顯示之方法，其中該最佳可視面係指於該最佳觀賞面上存在一面積為有限之可視面，於該面上只存在數量為有限之多數個最佳視點，該多數個最佳視點，係可對於左右眼，各自提供一具有低鬼影、與影像亮度接近之單一視景影像，該有限數量之最佳視點所構成之面，即為最佳可視面，對於存在於該最佳可視面上之任一位置，其x,y之座標值，係具有以下之關係：-x_max≦x≦x_max；-y_max≦y≦y_max；其中，x_max、y_max即規範該最佳可視面之範圍；另外，係於最佳觀賞面上，透過對3D影像作實際cross-talk與亮度之量測，可取得該x_max、y_max之值；根據該x_max、y_max，亦可如下式，以計算取得一水平可視角Ω_H、與一垂直可視角Ω_V：Ω_H=2×tan^-1(x_max/Z₀)；Ω_V=2×tan^-1(y_max/Z₀)；其中，Z₀為最佳觀賞距離；該x_max、y_max之值，亦可各自對應一i_max、k_max，使得存在於最佳可視面上之最佳可視點P_k,i,j，該P_k,i,j中之水平可視區編號i、垂直可視區編號k，係可具有以下之關係：|i|≦i_max；|k|≦k_max；其中，x_max、y_max與i_max、k_max、係具有以下之關係：x_max=i_max×n×L_E；y_max=k_max×L_V。The method of displaying a three-dimensional image according to claim 1, wherein the optimal visible surface means that a visible surface having a limited area exists on the optimal viewing surface, and only a limited number exists on the surface. The majority of the best viewpoints, the majority of the best viewpoints, for the left and right eyes, each providing a single view image with a low ghost and close to the brightness of the image, the finite number of best viewpoints, That is, the best visible surface, for any position existing on the optimal visible surface, the coordinate value of x, y has the following relationship: -x_max ≦x≦x_max ; -y_max ≦y≦ y_max ; wherein x_max , y_max is the range of the optimal visible surface; in addition, on the best viewing surface, the x_max can be obtained by measuring the actual cross-talk and brightness of the 3D image. And the value of y_max ; according to the x_max , y_max , the following equation can also be used to calculate a horizontal view angle Ω_H , and a vertical view angle Ω_V : Ω_H = 2 × tan^-1 (x_max / Z₀ ); Ω_V = 2 × tan^-1 (y_max / Z₀ ); wherein Z₀ is the optimal viewing distance; the x_max , y_max The values may also correspond to an i_max , k_max , such that the best visible point P_k,i,j existing on the optimal visible surface, the horizontal visible area number i in the P_k,i,j , and the vertical visible The region number k may have the following relationship: |i|≦i_max ;|k|≦k_max ; where x_max , y_max and i_max , k_max , have the following relationship: x_max =i_max ×n×L_E ;y_max =k_max ×L_V .